Q. Souza - Academia.edu (original) (raw)
Papers by Q. Souza
Reports on Mathematical Physics, 2007
International Journal of Theoretical Physics, 1996
Foundations of Physics, 1993
In this paper we formulate Einstein's gravitational theory with the Clifford bundle formalis... more In this paper we formulate Einstein's gravitational theory with the Clifford bundle formalism. The formalism suggests interpreting the gravitational field in the sense of Faraday, i.e., with the field residing in Minkowski spacetime. We succeeded in discovering the condition for this interpretation to hold. For the variables that play the role of the gravitational field in our theory, the Lagrangian
Clifford Algebras and Spinor Structures, 1995
In this paper we show that spinor fields with the right transformation properties and also supern... more In this paper we show that spinor fields with the right transformation properties and also supernelds can be represented as equivalence classes of exterior algebra fields. We construct explicitly these spinors for Lorentzian manifolds and present superfields through the hyperbolic Clifford algebra bundle (some interesting results concerning to this structure are presented) and its associated real spinor bundle. We compare our spinor fields with Crumeyrolle’s amorphic spinors (ideal sections of a Clifford algebra bundle) and also Dirac-Kahler spinors (sections of a Clifford algebra bundle) which cannot be used in physical theories of spinning matter.
In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan s... more In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the RCST), thereby being certain particular sections of a new bundle named Spin-Clifford bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to the famous Geroch's theorem concerning to the existence of spinor structures in a Lorentzian spacetime. We introduce also the covariant and algebraic Dirac spinor fields and compare these with DHSF, showing that all the three kinds of spinor fields contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-Kähler spinor fields are of this type), showing that they cannot be used to describe fermionic fields. We develop a rigorous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle (CB)) and of Dirac-Hestenes spinor fields. We show how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of a RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.
Gravitation the Spacetime Structure Silarg Viii, 1994
Using a Clifford bundle formalism, we examine: (a) the strong conditions for existence of conserv... more Using a Clifford bundle formalism, we examine: (a) the strong conditions for existence of conservation laws involving only the energy-momentum and angular momentum of the matter fields on a general Riemann-Cartan spacetime and the particular cases of Lorentzian and teleparallel spacetimes and (b) the conditions for the existence of conservation laws of energy-momentum and angular momentum for the matter and gravitational fields when this later concept can be rigorously defined. We examine in more details some statements concerning the issues of the conservation laws in General Relativity and Riemann-Cartan (including the particular case of the teleparallel ones) theories.
International Journal of Modern Physics D, 2005
7 Comments on the 'Evans Lemma' 8 Clifford Bundles Cℓ(T * M) and Cℓ(T M) 8.1 Clifford product, sc... more 7 Comments on the 'Evans Lemma' 8 Clifford Bundles Cℓ(T * M) and Cℓ(T M) 8.1 Clifford product, scalar contraction and exterior products. .. .
In this paper using a Clifford bundle formalism we examine (a): the strong conditions for existen... more In this paper using a Clifford bundle formalism we examine (a): the strong conditions for existence of conservation laws involving only the energy-momentum and angular momentum of the matter fields on a general Riemann-Cartan spacetime and also in the particular cases of Lorentzian and teleparallel spacetimes and (b): the conditions for the existence of conservation laws of energy-momentum and angular momentum for the matter and gravitational fields when this latter concept can be rigorously defined. We examine in details some misleading and even erroneous and often quoted statements concerning the issues of the conservation laws in General Relativity and Riemann-Cartan (including the particular case of the teleparallel one) theories.
Solid State Communications, 1986
ABSTRACT The variation of the lowest direct band gap of compounds CdSexTe1-x with hydrostatic pre... more ABSTRACT The variation of the lowest direct band gap of compounds CdSexTe1-x with hydrostatic pressure has been measured by photoluminescence at room temperature. This allowed determination of pressure dependence of the bowing parameter. Our data compared to theoretical calculations based on the dielectric model indicates that the average ionic potential is constant with pressure. This result has been previously assumed in the calculation of energy-band pressure coefficients and proved fundamental for the agreement with experimental values for a wide variety of semiconductors.
Foundations of Physics, 1995
We give a precise and modern mathematical characterization of the Newtonian spacetOne structure (... more We give a precise and modern mathematical characterization of the Newtonian spacetOne structure (N). Our formulation clarifies the concepts of absohtte space, Newton's relative spaces, and absolute tone. The concept of reference frames (which are "timelike" vector fieMs on N) plays a fundamental role in our approach, and the classification of all possible reference frames on ~ is O,vestigated in detail. We succeed #i identifying a Lorentzian structure on ~1 and we study the classical electrodynamics of Maxwell and Lorentz relative to this structure, obtahffng the #nportant result that there exists only one #1trinsic generalization of the Lorentz force law which is compatible with Maxwell equations. This is at variance with other proposed #1trinsic generalizations of the Loreutz force law appearing #z the literature. We present also a formulation of Newtonian gravitational theoo, as a curve spacetime theory and discuss its meaning. 2.1. Geometrical Structure 2.2. Newtonian Dynamics 3. Reference and Moving Frames 3.1. Reference Frames 3.2. Moving Frames 3.3. Newtonian Space and Newtonian Time. Relative Rest Spaces 3.4. Galileo's Principle of Relativity
International Journal of Theoretical Physics, 1996
In this paper we study Dirac-Hestenes spinor elds (DHSF) on a four-dimensional Riemann-Cartan spa... more In this paper we study Dirac-Hestenes spinor elds (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these elds must be dened as certain equivalence classes of even sectionsof the Cliord bundle (over the RCST), thereby being certain particular sections of a new bundle named Spin-Cliord bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to the famous Geroch's theorem concerning to the existence of spinor structures in a Lorentzian spacetime. We i n troduce also the covariant and algebraic Dirac spinor elds and compare these with DHSF, showing that all the three kinds of spinor elds contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-K ahler spinor elds are of this type), showing that they cannot be used to describe fermionic elds. We develop a rigorous theory for the covariant derivatives of Cliord elds (sections of the Cliord bundle (CB)) and of Dirac-Hestenes spinor elds. We show h o w to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of a RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian eld theory in the Cliord bundle.
International Journal of Theoretical Physics, 1996
In this paper we study Dirac-Hestenes spinor elds (DHSF) on a four-dimensional Riemann-Cartan spa... more In this paper we study Dirac-Hestenes spinor elds (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these elds must be dened as certain equivalence classes of even sectionsof the Cliord bundle (over the RCST), thereby being certain particular sections of a new bundle named Spin-Cliord bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to the famous Geroch's theorem concerning to the existence of spinor structures in a Lorentzian spacetime. We i n troduce also the covariant and algebraic Dirac spinor elds and compare these with DHSF, showing that all the three kinds of spinor elds contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-K ahler spinor elds are of this type), showing that they cannot be used to describe fermionic elds. We develop a rigorous theory for the covariant derivatives of Cliord elds (sections of the Cliord bundle (CB)) and of Dirac-Hestenes spinor elds. We show h o w to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of a RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian eld theory in the Cliord bundle.
Foundations of Physics, 1993
In this paper we formulate Einstein's gravitational theory with the Clifford bundle formalism. Th... more In this paper we formulate Einstein's gravitational theory with the Clifford bundle formalism. The formalism suggests interpreting the gravitational field in the sense of Faraday, i.e., with the field residing in Minkowski spacetime. We succeeded in discovering the condition for this interpretation to hold. For the variables that play the role of the gravitational field in our theory, the Lagrangian density turns out to be of the Yang-Mills type (with an auto-interaction plus gauge-fixing terms). We give a brief comparison of our theory with other field theories of the gravitational field in the flat Minkowski spacetime.
Reports on Mathematical Physics, 2007
In this paper we introduce the Dirac and spin-Dirac operators associated to a connection on Riema... more In this paper we introduce the Dirac and spin-Dirac operators associated to a connection on Riemann-Cartan space(time) and standard Dirac and spin-Dirac operators associated with a Levi-Civita connection on a Riemannian (Lorentzian) space(time) and calculate the square of these operators, which play an important role in several topics of modern Mathematics, in particular in the study of the geometry of moduli spaces of a class of black holes, the geometry of NS-5 brane solutions of type II supergravity theories and BPS solitons in some string theories. We obtain a generalized Lichnerowicz formula, decompositions of the Dirac and spin-Dirac operators and their squares in terms of the standard Dirac and spin-Dirac operators and using the fact that spinor fields (sections of a spin-Clifford bundle) have representatives in the Clifford bundle we present also a noticeable relation involving the spin-Dirac and the Dirac operators.
Clifford Algebras and Spinor Structures, 1995
Reports on Mathematical Physics, 2007
International Journal of Theoretical Physics, 1996
Foundations of Physics, 1993
In this paper we formulate Einstein's gravitational theory with the Clifford bundle formalis... more In this paper we formulate Einstein's gravitational theory with the Clifford bundle formalism. The formalism suggests interpreting the gravitational field in the sense of Faraday, i.e., with the field residing in Minkowski spacetime. We succeeded in discovering the condition for this interpretation to hold. For the variables that play the role of the gravitational field in our theory, the Lagrangian
Clifford Algebras and Spinor Structures, 1995
In this paper we show that spinor fields with the right transformation properties and also supern... more In this paper we show that spinor fields with the right transformation properties and also supernelds can be represented as equivalence classes of exterior algebra fields. We construct explicitly these spinors for Lorentzian manifolds and present superfields through the hyperbolic Clifford algebra bundle (some interesting results concerning to this structure are presented) and its associated real spinor bundle. We compare our spinor fields with Crumeyrolle’s amorphic spinors (ideal sections of a Clifford algebra bundle) and also Dirac-Kahler spinors (sections of a Clifford algebra bundle) which cannot be used in physical theories of spinning matter.
In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan s... more In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the RCST), thereby being certain particular sections of a new bundle named Spin-Clifford bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to the famous Geroch's theorem concerning to the existence of spinor structures in a Lorentzian spacetime. We introduce also the covariant and algebraic Dirac spinor fields and compare these with DHSF, showing that all the three kinds of spinor fields contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-Kähler spinor fields are of this type), showing that they cannot be used to describe fermionic fields. We develop a rigorous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle (CB)) and of Dirac-Hestenes spinor fields. We show how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of a RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.
Gravitation the Spacetime Structure Silarg Viii, 1994
Using a Clifford bundle formalism, we examine: (a) the strong conditions for existence of conserv... more Using a Clifford bundle formalism, we examine: (a) the strong conditions for existence of conservation laws involving only the energy-momentum and angular momentum of the matter fields on a general Riemann-Cartan spacetime and the particular cases of Lorentzian and teleparallel spacetimes and (b) the conditions for the existence of conservation laws of energy-momentum and angular momentum for the matter and gravitational fields when this later concept can be rigorously defined. We examine in more details some statements concerning the issues of the conservation laws in General Relativity and Riemann-Cartan (including the particular case of the teleparallel ones) theories.
International Journal of Modern Physics D, 2005
7 Comments on the 'Evans Lemma' 8 Clifford Bundles Cℓ(T * M) and Cℓ(T M) 8.1 Clifford product, sc... more 7 Comments on the 'Evans Lemma' 8 Clifford Bundles Cℓ(T * M) and Cℓ(T M) 8.1 Clifford product, scalar contraction and exterior products. .. .
In this paper using a Clifford bundle formalism we examine (a): the strong conditions for existen... more In this paper using a Clifford bundle formalism we examine (a): the strong conditions for existence of conservation laws involving only the energy-momentum and angular momentum of the matter fields on a general Riemann-Cartan spacetime and also in the particular cases of Lorentzian and teleparallel spacetimes and (b): the conditions for the existence of conservation laws of energy-momentum and angular momentum for the matter and gravitational fields when this latter concept can be rigorously defined. We examine in details some misleading and even erroneous and often quoted statements concerning the issues of the conservation laws in General Relativity and Riemann-Cartan (including the particular case of the teleparallel one) theories.
Solid State Communications, 1986
ABSTRACT The variation of the lowest direct band gap of compounds CdSexTe1-x with hydrostatic pre... more ABSTRACT The variation of the lowest direct band gap of compounds CdSexTe1-x with hydrostatic pressure has been measured by photoluminescence at room temperature. This allowed determination of pressure dependence of the bowing parameter. Our data compared to theoretical calculations based on the dielectric model indicates that the average ionic potential is constant with pressure. This result has been previously assumed in the calculation of energy-band pressure coefficients and proved fundamental for the agreement with experimental values for a wide variety of semiconductors.
Foundations of Physics, 1995
We give a precise and modern mathematical characterization of the Newtonian spacetOne structure (... more We give a precise and modern mathematical characterization of the Newtonian spacetOne structure (N). Our formulation clarifies the concepts of absohtte space, Newton's relative spaces, and absolute tone. The concept of reference frames (which are "timelike" vector fieMs on N) plays a fundamental role in our approach, and the classification of all possible reference frames on ~ is O,vestigated in detail. We succeed #i identifying a Lorentzian structure on ~1 and we study the classical electrodynamics of Maxwell and Lorentz relative to this structure, obtahffng the #nportant result that there exists only one #1trinsic generalization of the Lorentz force law which is compatible with Maxwell equations. This is at variance with other proposed #1trinsic generalizations of the Loreutz force law appearing #z the literature. We present also a formulation of Newtonian gravitational theoo, as a curve spacetime theory and discuss its meaning. 2.1. Geometrical Structure 2.2. Newtonian Dynamics 3. Reference and Moving Frames 3.1. Reference Frames 3.2. Moving Frames 3.3. Newtonian Space and Newtonian Time. Relative Rest Spaces 3.4. Galileo's Principle of Relativity
International Journal of Theoretical Physics, 1996
In this paper we study Dirac-Hestenes spinor elds (DHSF) on a four-dimensional Riemann-Cartan spa... more In this paper we study Dirac-Hestenes spinor elds (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these elds must be dened as certain equivalence classes of even sectionsof the Cliord bundle (over the RCST), thereby being certain particular sections of a new bundle named Spin-Cliord bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to the famous Geroch's theorem concerning to the existence of spinor structures in a Lorentzian spacetime. We i n troduce also the covariant and algebraic Dirac spinor elds and compare these with DHSF, showing that all the three kinds of spinor elds contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-K ahler spinor elds are of this type), showing that they cannot be used to describe fermionic elds. We develop a rigorous theory for the covariant derivatives of Cliord elds (sections of the Cliord bundle (CB)) and of Dirac-Hestenes spinor elds. We show h o w to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of a RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian eld theory in the Cliord bundle.
International Journal of Theoretical Physics, 1996
In this paper we study Dirac-Hestenes spinor elds (DHSF) on a four-dimensional Riemann-Cartan spa... more In this paper we study Dirac-Hestenes spinor elds (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these elds must be dened as certain equivalence classes of even sectionsof the Cliord bundle (over the RCST), thereby being certain particular sections of a new bundle named Spin-Cliord bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to the famous Geroch's theorem concerning to the existence of spinor structures in a Lorentzian spacetime. We i n troduce also the covariant and algebraic Dirac spinor elds and compare these with DHSF, showing that all the three kinds of spinor elds contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-K ahler spinor elds are of this type), showing that they cannot be used to describe fermionic elds. We develop a rigorous theory for the covariant derivatives of Cliord elds (sections of the Cliord bundle (CB)) and of Dirac-Hestenes spinor elds. We show h o w to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of a RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian eld theory in the Cliord bundle.
Foundations of Physics, 1993
In this paper we formulate Einstein's gravitational theory with the Clifford bundle formalism. Th... more In this paper we formulate Einstein's gravitational theory with the Clifford bundle formalism. The formalism suggests interpreting the gravitational field in the sense of Faraday, i.e., with the field residing in Minkowski spacetime. We succeeded in discovering the condition for this interpretation to hold. For the variables that play the role of the gravitational field in our theory, the Lagrangian density turns out to be of the Yang-Mills type (with an auto-interaction plus gauge-fixing terms). We give a brief comparison of our theory with other field theories of the gravitational field in the flat Minkowski spacetime.
Reports on Mathematical Physics, 2007
In this paper we introduce the Dirac and spin-Dirac operators associated to a connection on Riema... more In this paper we introduce the Dirac and spin-Dirac operators associated to a connection on Riemann-Cartan space(time) and standard Dirac and spin-Dirac operators associated with a Levi-Civita connection on a Riemannian (Lorentzian) space(time) and calculate the square of these operators, which play an important role in several topics of modern Mathematics, in particular in the study of the geometry of moduli spaces of a class of black holes, the geometry of NS-5 brane solutions of type II supergravity theories and BPS solitons in some string theories. We obtain a generalized Lichnerowicz formula, decompositions of the Dirac and spin-Dirac operators and their squares in terms of the standard Dirac and spin-Dirac operators and using the fact that spinor fields (sections of a spin-Clifford bundle) have representatives in the Clifford bundle we present also a noticeable relation involving the spin-Dirac and the Dirac operators.
Clifford Algebras and Spinor Structures, 1995