Related papers: A classical field theory formulation for the numer…
In an exact quantum-mechanical framework, we show that expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge, and in the presence of classical sources, automatically lead to causal and retarded…
An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…
We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange…
We propose a novel framework that interprets the electromagnetic field as a manifestation of spacetime pseudo-curvature, bridging electromagnetism with the geometric principles of general relativity. By introducing modified field equations,…
We derive the covariant equations of motion for Maxwell field theory and electrodynamics in multiscale spacetimes with weighted Laplacian. An effective spacetime-dependent electric charge of geometric origin naturally emerges from the…
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first…
The Lagrangian formalism is used to derive covariant equations that are suitable for use in continuously distributed matter in curved spacetime. Special attention is given to theoretical representation, in which the Lagrangian and its…
We analyze the relation of the notion of a pluri-Lagrangian system, which recently emerged in the theory of integrable systems, to the classical notion of variational symmetry, due to E. Noether. We treat classical mechanical systems and…
We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point…
Canonical formulation of quantum field theory on the Light Front (LF) is reviewed. The problem of constructing the LF Hamiltonian which gives the theory equivalent to original Lorentz and gauge invariant one is considered. We describe…
The time dependent Dirac-Maxwell's Equations in presence of electric and magnetic sources are written in chiral media and the solutions for the classical problem are obtained in unique simple and consistent manner. The quaternion…
A general variational principle of classical fields with a Lagrangian containing the field quantity and its derivatives of up to the N-th order is presented. Noether's theorem is derived. The generalized Hamilton-Jacobi's equation for the…
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. It has in general case quaternion single structure, consisting of four independent field constituents, which differ with each other by…
The ordinary Landau problem consists of describing a charged particle in time-independent magnetic field. In the present case the problem is generalized onto time-dependent uniform electric fields with time-dependent mass and harmonic…
A quantization of field theory based on the DeDonder-Weyl covariant Hamiltonian formulation is discussed. A hypercomplex extension of quantum mechanics, in which the space-time Clifford algebra replaces that of the complex numbers, appears…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. Tey are reviewed in the work presented. It is drawing the attention on the following aspects. EM-field has in general case quaternion…
We generalize chiral perturbation theory with spinless matter fields in the fundamental representation of ${\rm SU}(N)$ to curved spacetime in the presence of an external gravitational field. This work is motivated by recent interest in…
In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton's formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to…
We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric…