Stoil Donev | Bulgarian Academy of Sciences (original) (raw)

Papers by Stoil Donev

This book aims to summarize in a consistent way the authors' results in attempting to build spati... more This book aims to summarize in a consistent way the authors' results in attempting to build spatially finite and time-stable models of photon-like objects through extending Maxwell vacuum equations to local energy-momentum exchange relations and making use of modern differential geometry. In particular, we interpret dynamically Frobenius integrability theory of distributions on manifolds through an appropriate ϕ-extension along p-vector fields of the classical Lie derivative, and give interaction interpretation of the nonintegrability of subdistributions of an integrable distribution recognizing physically these subdistributions as time-stable subsystems of the field object considered and formally presented by the integrable distribution. The space-time propagation of our photon-like object is, of course, along appropriate symmetry of the representing distribution.

This paper aims to present the pure field part of the newly developed nonlinear {\it Extended Ele... more This paper aims to present the pure field part of the newly developed nonlinear {\it Extended Electrodynamics} [1]-[3] in non-relativistic terms, i.e. in terms of the electric and magnetic vector fields (${\mathbf E},{\mathbf B}$), and to give explicitly those (3+1)-soliton solutions of the new equations which have the integral properties of photons. The set of solutions to the new equations contains all solutions to Maxwell's equations as a subclass, as well as, new solutions, called nonlinear. The important characteristics {\it scale factor}, {\it amplitude function}, and {\it phase function} of a nonlinear solution are defined in a coordinate free way and effectively used. The nonlinear solutions are identified through the non-zero values of two appropriately defined vector fields veccalF\vec{\cal F}veccalF and veccalM\vec{\cal M}veccalM, as well as, through the finite values of the corresponding scale factors. The intrinsic angular momentum (spin) is also defined. A limited superposition principle (interference of nonlinear solutions), yielding the well known classical {\it coherence} conditions, is found to exist.

This paper presents the transition from Classical Electrodynamics (CED) to Extended Electrodynami... more This paper presents the transition from Classical Electrodynamics (CED) to Extended Electrodynamics (EED) from the electromagnetic duality point of view, and emphasizes the role of the canonical complex structure in calR2{\cal R}^2calR2 in, both, nonrelativistic and relativistic formulations of CED and EED. We begin with summarizing the motivations for passing to EED, as well as we motivate and outline the way to be followed in pursuing the right extension of Maxwell equations. Further we give the nonrelativistic and relativistic approaches to the extension and give explicitly the new equations as well as some properties of the nonlinear vacuum solutions.

In this paper we show that the basic external (i.e. not determined by the equations) object in Cl... more In this paper we show that the basic external (i.e. not determined by the equations) object in Classical electrodynamics equations is a complex structure. In the 3-dimensional standard form of Maxwell equations this complex structure mathcalI\mathcal{I}mathcalI participates implicitly in the equations and its presence is responsible for the so called duality invariance. We give a new form of the equations showing explicitly the participation of mathcalI\mathcal{I}mathcalI. In the 4-dimensional formulation the complex structure is extracted directly from the equations, it appears as a linear map Phi\PhiPhi in the space of 2-forms on mathbbR4\mathbb{R}^4mathbbR4. It is shown also that Phi\PhiPhi may appear through the equivariance properties of the new formulation of the theory. Further we show how this complex structure Phi\PhiPhi combines with the Poincare isomorphism mathfrakP\mathfrak{P}mathfrakP between the 2-forms and 2-tensors to generate all well known and used in the theory (pseudo)metric constructions on mathbbR4\mathbb{R}^4mathbbR4, and to define the conformal symmetry properties. The equations of Extended Electrodynamics (EED) do not also need these pseudometrics as beforehand necessary structures. A new formulation of the EED equations in terms of a generalized Lie derivative is given.

This paper aims to give explicitly all non-linear vacuum solutions to our non-linear field equati... more This paper aims to give explicitly all non-linear vacuum solutions to our non-linear field equations, and to define in a coordinate free manner the important subclass of non-linear solutions, which we call almost photon-like. By means of a correct introduction of the local and integral intrinsic angular momentums of these solutions, we saparate the photon-like solutions through the requirement their integral intrinsic angular momentums to be equal to the Planck's constant. Finally, we consider such solutions, moving radially to or from a given center, using standard spherical coordinates.

In the present paper we give a brief study of the observed homology properties of the standard el... more In the present paper we give a brief study of the observed homology properties of the standard electromagnetic stress-energy-momentum tensor in the important case of null fields, i.e., when the two invariants I1 = 12FmunuFmunu and I2 = Fmunu(*F)munu are vanished. The importance of this special case is based on the fact that this is the only case, when the field and its energy tensor admit unique common null eigen-direction, defining the propagation direction. An additional motivation for the approach presented here comes from the so-called Extended Electrodynamics developed by the authors. In Extended Electrodynamics all nonlinear solutions in the vacuum case have zero invariants. Among the class of nonlinear solutions, there are spatially finite and time-stable spin carrying solutions with photon-like properties.

This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The re... more This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out in relativistic terms in Minkowski space-time. The non-linear vacuum solutions are considered and fully described. It is specially pointed out that solitary waves with various, in fact arbitrary, spatial structure and photon-like propagation properties exist. The {\it null} character of all non-linear vacuum solutions is established and extensively used further. Coordinate-free definitions are given to the important quantities {\it amplitude} and {\it phase}. The new quantity, named {\it scale factor}, is introduced and used as a criterion for availability of rotational component of propagation of some of the nonlinear, i.e. nonmaxwellian, vacuum solutions. The group structure properties of the nonlinear vacuum solutions are analyzed in some detail, showing explicitly the connection of the vacuum solutions with some complex valued functions. Connection-curvature interpretations are given and a special attention is paid to the curvature interpretation of the intrinsic rotational (spin) properties of some of the nonlinear solutions. Several approaches to coordinate-free local description and computation of the integral spin momentum are considered. Finally, a large family of nonvacuum spatial soliton-like solutions is explicitly written down, and a procedure to get (3+1) versions of the known (1+1) soliton solutions is obtained.

This paper aims to present a general idea for description of spatially finite physical objects wi... more This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and structures connected with the Frobenius integrability/nonintegrability theorems and electromagnetic strain quantities. The idea is based on consideration of {\it nonintegrable} subdistributions of some appropriate completely integrable distribution (differential system) on a manifold and then to make use of the corresponding curvatures and correspondingly directed strains as measures of interaction, i.e. of energy-momentum exchange among the physical subsystems mathematically represented by the nonintegrable subdistributions. The concept of photon-like object is introduced and description (including lagrangian) of such objects in these terms is given.

In this paper, in the frame of Extended Electrodynamics (EED), we study some of the consequences ... more In this paper, in the frame of Extended Electrodynamics (EED), we study some of the consequences that can be obtained from the introduced and used by Maxwell equations complex structure \mathcal{J} in the space of 2-forms on \mathbb{R}^4, and also used in EED. First we give the vacuum EED equations with some comments. Then we recall some facts about the invariance group GGG (with Lie algebra \mathcal{G}) of the standard complex structure JJJ in \mathbb{R}^2. After defining and briefly studying a representation of GGG in the space of 2-forms on \mathbb{R}^4 and the joint action of GGG in the space of \mathcal{G}-valued 2-forms on \mathbb{R}^4 we consider its connection with the vacuum solutions of EED. Finally we consider the case with point dependent group parameters and show that the set of the nonlinear vacuum EED solutions is a disjoint union of orbits of the GGG-action, noting some similarities with the quantim mechanical eigen picture and with the QFT creation and anihilation operators.

Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 1995

... Downloaded from rspa.royalsocietypublishing.org on November 12, 2010 Energy-momentum-directed... more ... Downloaded from rspa.royalsocietypublishing.org on November 12, 2010 Energy-momentum-directed nonlinearization of Maxwell's equations in the case of a continuous media By Stoil Donev1 and Maria Tashkova2 1 Institute for ... TCiiü1 ®ki-\-Q2® k2) = J?1 ® Kiki + П2® i\xk2 ...

This paper aims to present an elaborate view on the motivation and realization of the idea to ext... more This paper aims to present an elaborate view on the motivation and realization of the idea to extend Maxwell's electrodynamics to Extended Electrodynamics in a reasonable and appropriate way in order to make it possible to describe electromagnetic (3+1)-soliton-like objects in vacuum and in the presence of continuous media (external fields), exchanging energy-momentum with the electromagnetic field.

This paper considers a generalization of the existing concept of parallel (with respect to a give... more This paper considers a generalization of the existing concept of parallel (with respect to a given connection) geometric objects and its possible usage as a suggesting rule in searching for adequate field equations in theoretical physics. The generalization tries to represent mathematically the two-sided nature of the physical objects, the {\it change} and the {\it conservation}. The physical objects are presented mathematically by sections Psi\PsiPsi of vector bundles, the admissible changes DPsiD\PsiDPsi are described as a rsult of the action of appropriate differential operators DDD on these sections, and the conservation propertieis are accounted for by the requirement that suitable projections of DPsiD\PsiDPsi on Psi\PsiPsi and on other appropriate sections must be zero. It is shown that the most important equations of theoretical physics obey this rule. Extended forms of Maxwell and Yang-Mills equations are also considered.

This paper aims to review our recent results on exploring the capabilities of non-quantum field t... more This paper aims to review our recent results on exploring the capabilities of non-quantum field theory as a possible tool for describing single photon-like objects, considered as massless time-stable spatially finite physical entities with compatible translational-rotational dynamical structure. The main idea is to interpret the local physical interaction as available Frobenius curvature. It consists of five chapters and includes 22 sections and subsections.

This paper aims to show that making use of Newton's view on equations of motion of a physical sys... more This paper aims to show that making use of Newton's view on equations of motion of a physical system and of the Maxwell stress tensor we come to a natural nonlinearization of Maxwell equations in vacuum making use only of nonrelativistic terms. The new equations include all Maxwell solutions plus new ones, among which one may find time-stable and spatially finite ones with photon-like properties and behavior.

This paper aims to consider the general properties of the non-linear solutions to the vacuum equa... more This paper aims to consider the general properties of the non-linear solutions to the vacuum equations of Extended Electrodynamics. The *-invariance and the conformal invariance of the equations are mentioned. It is also proved that all non-linear solutions have zero invariants: F_{\mu\nu}F^{\mu\nu} = (*F)_{\mu\nu}F^{\mu\nu} = 0. The three invariant characteristics of the non-linear solutions: amplitude, phase and scale factor are introdiced and discussed.

Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 1993

This paper aims to present a general idea for description of spatially finite physical objects wi... more This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and structures connected with the Frobenius integrability/nonintegrability theorems given in terms of distributions on manifolds with corresponding curvature defined by the Nijenhuis operator. The idea is based on consideration of {\it nonintegrable} subdistributions of some appropriate completely integrable distribution (differential system) on a manifold and then to make use of the corresponding curvatures as generators of measures of interaction, i.e. of energy-momentum exchange among the physical subsystems mathematically represented by the nonintegrable subdistributions. The concept of photon-like object is introduced and description of such objects in these terms is given.

This paper presents an attempt to come to a natural field model of individual photons considered ... more This paper presents an attempt to come to a natural field model of individual photons considered as finite entities and propagating along some distinguished direction in space in a consistent translational-rotational manner. The starting assumption reflects their most trustful property to propagate translationally in a uniform way along straight lines. The model gives correct energy-momentum characteristics and connects the rotational characteristics of photons with corresponding nonintegrability (or curvature) of some 2-dimensional distributions (or Pfaff systems) on mathbbR4\mathbb{R}^4mathbbR4. It is obtained that the curvature is proportional to the corresponding energy-density. The field equations are obtained through a Lagrangian and they express a consistency condition between photon's translational and rotational propagation properties. The energy tensor is deduced directly from the equations since the corresponding Hilbert energy-tensor becomes zero on the solutions. Planck's formula E=hnuE=h\nuE=hnu is naturally obtained as an integral translational-rotational consistency relation.

This paper presents an alternative relativistic nonlinear approach to the vacuum case of classica... more This paper presents an alternative relativistic nonlinear approach to the vacuum case of classical electrodynamics. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature. So, they must represent local energy-momentum balance relations. Formally, the new equations are in terms of appropriately extended Lie derivative of R 2 -valued differential 2-form along a R 2 -valued 2-vector on Minkowski space-time.

This paper presents an alternative to the Maxwell vacuum equations pre-relativistic approach to d... more This paper presents an alternative to the Maxwell vacuum equations pre-relativistic approach to description of electromagnetic field objects. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature and the physical relations represented by them should represent local stress-energy-momentum balance relations. Such a view does not go along with the classical assumption for local recognizability of the electric and magnetic constituents E and B as time-stable and space propagationg subsystems of the field objects. The corresponding reconsideration brought us to the assumption, that the two couples (E, B) and (−B, E) are much more adequate in this respect: free electromagnetic field objects exist in a permanent propagation with the fundamental velocity c, so each of its recognizable subsystems should be able to carry momentum, and neither E nor B are able to do this separately, while each of the couples (E, B; −B, E) is able to do this, but only in presence of the other. Therefore, the necessary internal local dynamics, admissible changes, time stability and recognizability during space propagation should be viewed in terms of (E, B) and (−B, E) and their mutually compatible changes.

This book aims to summarize in a consistent way the authors' results in attempting to build spati... more This book aims to summarize in a consistent way the authors' results in attempting to build spatially finite and time-stable models of photon-like objects through extending Maxwell vacuum equations to local energy-momentum exchange relations and making use of modern differential geometry. In particular, we interpret dynamically Frobenius integrability theory of distributions on manifolds through an appropriate ϕ-extension along p-vector fields of the classical Lie derivative, and give interaction interpretation of the nonintegrability of subdistributions of an integrable distribution recognizing physically these subdistributions as time-stable subsystems of the field object considered and formally presented by the integrable distribution. The space-time propagation of our photon-like object is, of course, along appropriate symmetry of the representing distribution.

This paper aims to present the pure field part of the newly developed nonlinear {\it Extended Ele... more This paper aims to present the pure field part of the newly developed nonlinear {\it Extended Electrodynamics} [1]-[3] in non-relativistic terms, i.e. in terms of the electric and magnetic vector fields (${\mathbf E},{\mathbf B}$), and to give explicitly those (3+1)-soliton solutions of the new equations which have the integral properties of photons. The set of solutions to the new equations contains all solutions to Maxwell's equations as a subclass, as well as, new solutions, called nonlinear. The important characteristics {\it scale factor}, {\it amplitude function}, and {\it phase function} of a nonlinear solution are defined in a coordinate free way and effectively used. The nonlinear solutions are identified through the non-zero values of two appropriately defined vector fields veccalF\vec{\cal F}veccalF and veccalM\vec{\cal M}veccalM, as well as, through the finite values of the corresponding scale factors. The intrinsic angular momentum (spin) is also defined. A limited superposition principle (interference of nonlinear solutions), yielding the well known classical {\it coherence} conditions, is found to exist.

This paper presents the transition from Classical Electrodynamics (CED) to Extended Electrodynami... more This paper presents the transition from Classical Electrodynamics (CED) to Extended Electrodynamics (EED) from the electromagnetic duality point of view, and emphasizes the role of the canonical complex structure in calR2{\cal R}^2calR2 in, both, nonrelativistic and relativistic formulations of CED and EED. We begin with summarizing the motivations for passing to EED, as well as we motivate and outline the way to be followed in pursuing the right extension of Maxwell equations. Further we give the nonrelativistic and relativistic approaches to the extension and give explicitly the new equations as well as some properties of the nonlinear vacuum solutions.

In this paper we show that the basic external (i.e. not determined by the equations) object in Cl... more In this paper we show that the basic external (i.e. not determined by the equations) object in Classical electrodynamics equations is a complex structure. In the 3-dimensional standard form of Maxwell equations this complex structure mathcalI\mathcal{I}mathcalI participates implicitly in the equations and its presence is responsible for the so called duality invariance. We give a new form of the equations showing explicitly the participation of mathcalI\mathcal{I}mathcalI. In the 4-dimensional formulation the complex structure is extracted directly from the equations, it appears as a linear map Phi\PhiPhi in the space of 2-forms on mathbbR4\mathbb{R}^4mathbbR4. It is shown also that Phi\PhiPhi may appear through the equivariance properties of the new formulation of the theory. Further we show how this complex structure Phi\PhiPhi combines with the Poincare isomorphism mathfrakP\mathfrak{P}mathfrakP between the 2-forms and 2-tensors to generate all well known and used in the theory (pseudo)metric constructions on mathbbR4\mathbb{R}^4mathbbR4, and to define the conformal symmetry properties. The equations of Extended Electrodynamics (EED) do not also need these pseudometrics as beforehand necessary structures. A new formulation of the EED equations in terms of a generalized Lie derivative is given.

This paper aims to give explicitly all non-linear vacuum solutions to our non-linear field equati... more This paper aims to give explicitly all non-linear vacuum solutions to our non-linear field equations, and to define in a coordinate free manner the important subclass of non-linear solutions, which we call almost photon-like. By means of a correct introduction of the local and integral intrinsic angular momentums of these solutions, we saparate the photon-like solutions through the requirement their integral intrinsic angular momentums to be equal to the Planck's constant. Finally, we consider such solutions, moving radially to or from a given center, using standard spherical coordinates.

In the present paper we give a brief study of the observed homology properties of the standard el... more In the present paper we give a brief study of the observed homology properties of the standard electromagnetic stress-energy-momentum tensor in the important case of null fields, i.e., when the two invariants I1 = 12FmunuFmunu and I2 = Fmunu(*F)munu are vanished. The importance of this special case is based on the fact that this is the only case, when the field and its energy tensor admit unique common null eigen-direction, defining the propagation direction. An additional motivation for the approach presented here comes from the so-called Extended Electrodynamics developed by the authors. In Extended Electrodynamics all nonlinear solutions in the vacuum case have zero invariants. Among the class of nonlinear solutions, there are spatially finite and time-stable spin carrying solutions with photon-like properties.

This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The re... more This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out in relativistic terms in Minkowski space-time. The non-linear vacuum solutions are considered and fully described. It is specially pointed out that solitary waves with various, in fact arbitrary, spatial structure and photon-like propagation properties exist. The {\it null} character of all non-linear vacuum solutions is established and extensively used further. Coordinate-free definitions are given to the important quantities {\it amplitude} and {\it phase}. The new quantity, named {\it scale factor}, is introduced and used as a criterion for availability of rotational component of propagation of some of the nonlinear, i.e. nonmaxwellian, vacuum solutions. The group structure properties of the nonlinear vacuum solutions are analyzed in some detail, showing explicitly the connection of the vacuum solutions with some complex valued functions. Connection-curvature interpretations are given and a special attention is paid to the curvature interpretation of the intrinsic rotational (spin) properties of some of the nonlinear solutions. Several approaches to coordinate-free local description and computation of the integral spin momentum are considered. Finally, a large family of nonvacuum spatial soliton-like solutions is explicitly written down, and a procedure to get (3+1) versions of the known (1+1) soliton solutions is obtained.

This paper aims to present a general idea for description of spatially finite physical objects wi... more This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and structures connected with the Frobenius integrability/nonintegrability theorems and electromagnetic strain quantities. The idea is based on consideration of {\it nonintegrable} subdistributions of some appropriate completely integrable distribution (differential system) on a manifold and then to make use of the corresponding curvatures and correspondingly directed strains as measures of interaction, i.e. of energy-momentum exchange among the physical subsystems mathematically represented by the nonintegrable subdistributions. The concept of photon-like object is introduced and description (including lagrangian) of such objects in these terms is given.

In this paper, in the frame of Extended Electrodynamics (EED), we study some of the consequences ... more In this paper, in the frame of Extended Electrodynamics (EED), we study some of the consequences that can be obtained from the introduced and used by Maxwell equations complex structure \mathcal{J} in the space of 2-forms on \mathbb{R}^4, and also used in EED. First we give the vacuum EED equations with some comments. Then we recall some facts about the invariance group GGG (with Lie algebra \mathcal{G}) of the standard complex structure JJJ in \mathbb{R}^2. After defining and briefly studying a representation of GGG in the space of 2-forms on \mathbb{R}^4 and the joint action of GGG in the space of \mathcal{G}-valued 2-forms on \mathbb{R}^4 we consider its connection with the vacuum solutions of EED. Finally we consider the case with point dependent group parameters and show that the set of the nonlinear vacuum EED solutions is a disjoint union of orbits of the GGG-action, noting some similarities with the quantim mechanical eigen picture and with the QFT creation and anihilation operators.

Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 1995

... Downloaded from rspa.royalsocietypublishing.org on November 12, 2010 Energy-momentum-directed... more ... Downloaded from rspa.royalsocietypublishing.org on November 12, 2010 Energy-momentum-directed nonlinearization of Maxwell's equations in the case of a continuous media By Stoil Donev1 and Maria Tashkova2 1 Institute for ... TCiiü1 ®ki-\-Q2® k2) = J?1 ® Kiki + П2® i\xk2 ...

This paper aims to present an elaborate view on the motivation and realization of the idea to ext... more This paper aims to present an elaborate view on the motivation and realization of the idea to extend Maxwell's electrodynamics to Extended Electrodynamics in a reasonable and appropriate way in order to make it possible to describe electromagnetic (3+1)-soliton-like objects in vacuum and in the presence of continuous media (external fields), exchanging energy-momentum with the electromagnetic field.

This paper considers a generalization of the existing concept of parallel (with respect to a give... more This paper considers a generalization of the existing concept of parallel (with respect to a given connection) geometric objects and its possible usage as a suggesting rule in searching for adequate field equations in theoretical physics. The generalization tries to represent mathematically the two-sided nature of the physical objects, the {\it change} and the {\it conservation}. The physical objects are presented mathematically by sections Psi\PsiPsi of vector bundles, the admissible changes DPsiD\PsiDPsi are described as a rsult of the action of appropriate differential operators DDD on these sections, and the conservation propertieis are accounted for by the requirement that suitable projections of DPsiD\PsiDPsi on Psi\PsiPsi and on other appropriate sections must be zero. It is shown that the most important equations of theoretical physics obey this rule. Extended forms of Maxwell and Yang-Mills equations are also considered.

This paper aims to review our recent results on exploring the capabilities of non-quantum field t... more This paper aims to review our recent results on exploring the capabilities of non-quantum field theory as a possible tool for describing single photon-like objects, considered as massless time-stable spatially finite physical entities with compatible translational-rotational dynamical structure. The main idea is to interpret the local physical interaction as available Frobenius curvature. It consists of five chapters and includes 22 sections and subsections.

This paper aims to show that making use of Newton's view on equations of motion of a physical sys... more This paper aims to show that making use of Newton's view on equations of motion of a physical system and of the Maxwell stress tensor we come to a natural nonlinearization of Maxwell equations in vacuum making use only of nonrelativistic terms. The new equations include all Maxwell solutions plus new ones, among which one may find time-stable and spatially finite ones with photon-like properties and behavior.

This paper aims to consider the general properties of the non-linear solutions to the vacuum equa... more This paper aims to consider the general properties of the non-linear solutions to the vacuum equations of Extended Electrodynamics. The *-invariance and the conformal invariance of the equations are mentioned. It is also proved that all non-linear solutions have zero invariants: F_{\mu\nu}F^{\mu\nu} = (*F)_{\mu\nu}F^{\mu\nu} = 0. The three invariant characteristics of the non-linear solutions: amplitude, phase and scale factor are introdiced and discussed.

Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 1993

This paper aims to present a general idea for description of spatially finite physical objects wi... more This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and structures connected with the Frobenius integrability/nonintegrability theorems given in terms of distributions on manifolds with corresponding curvature defined by the Nijenhuis operator. The idea is based on consideration of {\it nonintegrable} subdistributions of some appropriate completely integrable distribution (differential system) on a manifold and then to make use of the corresponding curvatures as generators of measures of interaction, i.e. of energy-momentum exchange among the physical subsystems mathematically represented by the nonintegrable subdistributions. The concept of photon-like object is introduced and description of such objects in these terms is given.

This paper presents an attempt to come to a natural field model of individual photons considered ... more This paper presents an attempt to come to a natural field model of individual photons considered as finite entities and propagating along some distinguished direction in space in a consistent translational-rotational manner. The starting assumption reflects their most trustful property to propagate translationally in a uniform way along straight lines. The model gives correct energy-momentum characteristics and connects the rotational characteristics of photons with corresponding nonintegrability (or curvature) of some 2-dimensional distributions (or Pfaff systems) on mathbbR4\mathbb{R}^4mathbbR4. It is obtained that the curvature is proportional to the corresponding energy-density. The field equations are obtained through a Lagrangian and they express a consistency condition between photon's translational and rotational propagation properties. The energy tensor is deduced directly from the equations since the corresponding Hilbert energy-tensor becomes zero on the solutions. Planck's formula E=hnuE=h\nuE=hnu is naturally obtained as an integral translational-rotational consistency relation.

This paper presents an alternative relativistic nonlinear approach to the vacuum case of classica... more This paper presents an alternative relativistic nonlinear approach to the vacuum case of classical electrodynamics. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature. So, they must represent local energy-momentum balance relations. Formally, the new equations are in terms of appropriately extended Lie derivative of R 2 -valued differential 2-form along a R 2 -valued 2-vector on Minkowski space-time.

This paper presents an alternative to the Maxwell vacuum equations pre-relativistic approach to d... more This paper presents an alternative to the Maxwell vacuum equations pre-relativistic approach to description of electromagnetic field objects. Our view is based on the understanding that the corresponding differential equations should be dynamical in nature and the physical relations represented by them should represent local stress-energy-momentum balance relations. Such a view does not go along with the classical assumption for local recognizability of the electric and magnetic constituents E and B as time-stable and space propagationg subsystems of the field objects. The corresponding reconsideration brought us to the assumption, that the two couples (E, B) and (−B, E) are much more adequate in this respect: free electromagnetic field objects exist in a permanent propagation with the fundamental velocity c, so each of its recognizable subsystems should be able to carry momentum, and neither E nor B are able to do this separately, while each of the couples (E, B; −B, E) is able to do this, but only in presence of the other. Therefore, the necessary internal local dynamics, admissible changes, time stability and recognizability during space propagation should be viewed in terms of (E, B) and (−B, E) and their mutually compatible changes.