16 research outputs found
The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2
The structure properties of multidimensional Delsarte transmutation operators
in parametirc functional spaces are studied by means of differential-geometric
tools. It is shown that kernels of the corresponding integral operator
expressions depend on the topological structure of related homological cycles
in the coordinate space. As a natural realization of the construction presented
we build pairs of Lax type commutive differential operator expressions related
via a Darboux-Backlund transformation having a lot of applications in solition
theory. Some results are also sketched concerning theory of Delsarte
transmutation operators for affine polynomial pencils of multidimensional
differential operators.Comment: 10 page
The Electromagnetic Lorentz Problem and the Hamiltonian Structure Analysis of the Maxwell-Yang-Mills Type Dynamical Systems within the Reduction Method
Based on analysis of reduced geometric structures on fi bered manifolds, invariant under action of an abelian functional symmetry group, we construct the symplectic structures associated with connection forms on the related principal fi ber bundles with abelian functional structure groups. The Marsden-Weinstein reduction procedure is applied to the Maxwell and Yang-Mills type dynamical systems. The geometric properties of Lorentz type constraints, describing the electromagnetic fi eld properties in vacuum and related
with the well known Dirac-Fock-Podolsky problem, are discussed
The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited
A differential-algebraic approach to studying the Lax type integrability of
the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax
type representation and Poisson structures constructed in exact form. The
related bi-Hamiltonian integrability and compatible Poissonian structures of
the generalized Riemann type hierarchy are also discussed.Comment: 18 page
The Electromagnetic Lorentz Condition Problem and Symplectic Properties of Maxwell and Yang-Mills Type Dynamical Systems
Symplectic structures associated to connection forms on certain types of
principal fiber bundles are constructed via analysis of reduced geometric
structures on fibered manifolds invariant under naturally related symmetry
groups. This approach is then applied to nonstandard Hamiltonian analysis of of
dynamical systems of Maxwell and Yang-Mills type. A symplectic reduction theory
of the classical Maxwell equations is formulated so as to naturally include the
Lorentz condition (ensuring the existence of electromagnetic waves), thereby
solving the well known Dirac -Fock - Podolsky problem. Symplectically reduced
Poissonian structures and the related classical minimal interaction principle
for the Yang-Mills equations are also considered. 1
The Relativistic Electrodynamics Least Action Principles Revisited: New Charged Point Particle and Hadronic String Models Analysis
The classical relativistic least action principle is revisited from the
vacuum field theory approach. New physically motivated versions of relativistic
Lorentz type forces are derived, a new relativistic hadronic string model is
proposed and analyzed in detail.Comment: n/
The Vacuum Structure, Special Relativity and Quantum Mechanics Revisited: a Field Theory No-Geometry Approach within the Lagrangian and Hamiltonian Formalisms. Part 2
The main fundamental principles characterizing the vacuum field structure are
formulated and the modeling of the related vacuum medium and charged point
particle dynamics by means of devised field theoretic tools are analyzed. The
work is devoted to studying the vacuum structure, special relativity,
electrodynamics of interacting charged point particles and quantum mechanics,
and is a continuation of \cite{BPT,BRT1}. Based on the vacuum field theory
no-geometry approach, the Lagrangian and Hamiltonian reformulation of some
alternative classical 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.Comment: 11 page