THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS THE VACUUM STRUCTURE, SPECIAL RELATIVITY AND QUANTUM MECHANICS REVISITED: A FIELD THEORY NO-GEOMETRY APPROACH WITHIN THE LAGRANGIAN AND HAMILTONIAN FORMALISMS. Part 2 (original) (raw)
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2010
The work is devoted to studying the vacuum structure, special relativity, electrodynamics of inter acting charged point particles and quantum mechanics, and is a continuation of . Based on the vacuum field theory no geometry approach, the Lagrangian and Hamiltonian reformulation of some alternative clas sical electrodynamics models is devised. The Dirac type quantization procedure, based on the canonical Hamiltonian formulation, is developed for some alternative electrodynamics models. Within an approach developed a possibility of the combined description both of electrodynamics and gravity is analyzed.
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry approach developed in [6,7,9], the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are devised. The Dirac-type quantization procedure for the considered alternative electrodynamics models, based on the obtained canonical Hamiltonian formulations, is developed. Comment: 9 pages
The Lagrangian and Hamiltonian Aspects of the Electrodynamic Vacuum-Field Theory Models
We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum- eld structure. We analyze the models of the vacuum eld medium and charged point particle dynamics using the developed eld theory concepts. There is also described a new approach to the classical Maxwell theory based on the derived and newly interpreted basic equations making use of the vacuum eld theory approach. In particular, there are obtained the main classical special relativity theory relations and their new explanations. The well known Feynman approach to Maxwell electromagnetic equations and the Lorentz type force derivation is also discussed in detail. A related charged point particle dynamics and a hadronic string model analysis is also presented. We also revisited and reanalyzed the classical Lorentz force expression in arbitrary non-inertial reference frames and present some new interpretations of the relations between special relativity theory and its quantum mechanical aspects. Some results related with the charge particle radia- tion problem and the magnetic potential topological aspects are discussed. The electromagnetic Dirac-Fock-Podolsky problem of the Maxwell and Yang-Mills type dynamical systems is ana- lyzed within the classical Dirac-Marsden-Weinstein symplectic reduction theory. The problem of constructing Fock type representations and retrieving their creation-annihilation operator struc- ture is analyzed. An application of the suitable current algebra representation to describing the non-relativistic Aharonov-Bohm paradox is presented. The current algebra coherent functional representations are constructed and their importance subject to the linearization problem of nonlinear dynamical systems in Hilbert spaces is demonstrated.
The Lagrangian and Hamiltonian properties of classical electrodynamics models and their associated Dirac quantizations are studied. Using the vacuum field theory approach developed in (Prykarpatsky et al. Theor. Math. Phys. 160(2): 1079– 1095, 2009 and The field structure of a vacuum,Maxwell equations and relativity theory aspects. Preprint ICTP) consistent canonical Hamiltonian reformulations of some alternative classical electrodynamics models are devised, and these formulations include the Lorentz condition in a natural way. The Dirac quantization procedure corresponding to the Hamiltonian formulations is developed. The crucial importance of the rest reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized. A concise expression for the Lorentz force is derived by suitably taking into account the duality of electromagnetic field and charged particle interactions. Finally, a physical explanation of the vacuum field medium and its relativistic properties fitting the mathematical framework developed is formulated and discussed.
Condensed Matter Physics, 2009
The work is devoted to the study of the Lagrangian and Hamiltonian properties of some relativistic electrodynamics models and is a continuation of our previous investigations. Based on the vacuum field theory approach, the Lagrangian and Hamiltonian reformulation of some classical electrodynamics models is devised. The Dirac type quantization procedure, based on the canonical Hamiltonian formulation, is developed. Within the approach proposed in the work a possibility of the combined description both of electrodynamics and gravity is analyzed.
2008
The main fundamental principles characterizing the vacuum field structure are formulated, the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The Maxwell electrodynamic theory is revisited and newly derived from the suggested vacuum field structure principles, the classical special relativity theory relationship between the energy and the corresponding point particle mass is revisited and newly obtained. The Lorentz force expression with respect to arbitrary non-inertial reference frames is revisited and discussed in detail, some new interpretations of relations between the special relativity theory and quantum mechanics are presented. The famous quantum-mechanical Schrödinger type equations for a relativistic point particle in the external potential and magnetic fields within the quasiclassical approximation as the Planck constant ħ→ 0 and the light velocity c→∞ are obtained.
We present new mathematical foundations of classical Maxwell–Lorentz electrodynamic models and related charged particles interaction-radiation problems, and analyze the fundamental least action principles via canonical Lagrangian and Hamiltonian formalisms. The corresponding electrodynamic vacuum field theory aspects of the classical Maxwell–Lorentz theory are analyzed in detail. Electrodynamic models of charged point particle dynamics based on a Maxwell type vacuum field medium description are described, and new field theory concepts related to the mass particle paradigms are discussed. We also revisit and reanalyze the mathematical structure of the classical Lorentz force expression with respect to arbitrary inertial reference frames and present new interpretations of some classical special relativity theory relationships.
Hamiltonian formulation of the theory of interacting gravitational and electron fields
Annals of Physics, 1978
The action which describes the interaction of gravitational and electron fields is expressed in canonical form. In addition to general covariance, it exhibits the local Lorentz invariance associated with four-dimensional rotations of the local orthonormal frames. The corresponding Hamiltonian constraints are derived and their (Dirac) bracket relations given. The derivative coupling of the gravitational tetrad and spinor fields is not present in the Hamiltonian, but rather in the unusual bracket relations of the field variables in the theory. If the timelike leg of the tetrad field is fixed to be normal to the x0 = constant hypersurfaces ("time gauge") the derivative coupling drops from the theory in the sense that the relation between the gravitational velocities and momenta is the same as when the spinor fields are absent.