Related papers: Kinematic Constraints in Generally Covariant Non-L…
When a set of particles are moving in a potential field, two aspects are concerned: 1) the relative motion of particle in spatial domain; 2) the particle velocity variations in time domain. The difficulty on treating the systems is…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined via the (Hamiltonian)…
We present a geometrical formulation of nonlinear electrodynamics by expressing its principal symbol as an optical metric-induced object. Under the assumption of no birefringence, we show that the evolution of linear perturbations can be…
Based on the Hamiltonian equation of motion of the $\phi^4$ theory with quenched disorder, we investigate the depinning phase transition of the domain-wall motion in two-dimensional magnets. With the short-time dynamic approach, we…
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
A description of electromagnetism as four-dimensional spacetime structure leads to the dynamics of a charged particle being determined only by the four-vector potential and the existence of an electromagnetic field depending on the…
This book is an attempt to build a consistent relativistic quantum theory of interacting particles. In the first part of the book "Quantum electrodynamics" we follow rather traditional approach to particle physics. Our discussion proceeds…
A complete perturbative expansion for the Hamiltonian describing the motion of a quantomechanical system constrained to move on an arbitrary submanifold of its configuration space $R^n$ is obtained.
The motion of a system of particles under electromagnetic interaction is considered. Under the assumption that the force acting on an electric charge is given by the sum of the electromagnetic fields produced by any other charged particles…
The un-reduction procedure introduced previously in the context of Mechanics is extended to covariant Field Theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one…
We discuss the motion of electrically and magnetically charged particles in the electromagnetic swirling universe. We show that the equations of motion can be decoupled in the Hamilton-Jacobi formalism, revealing the existence of a fourth…
One of the hardest problems to tackle in the dynamics of canonical approaches to quantum gravity is that of the Hamiltonian constraint. We investigate said problem in the context of formal geometric quantization. We study the implications…
We address the deformation quantization of generally parametrized systems displaying a natural time variable. The purpose of this exercise is twofold: first, to illustrate through a pedagogical example the potential of quantum phase space…
We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and…
Vlasov kinetic theory is the dynamics of a bunch of particles flowing according to symplectic Hamiltonian dynamics. More recently, this geometry has been extended to contact Hamiltonian dynamics. In this paper, we introduce geometric…
Non-linear electrodynamic models are re-assessed in this paper to pursue an investigation of the kinematics of the Compton effect in a magnetic background. Before considering specific models, we start off by presenting a general non-linear…
We are interested in the energy-momentum relation for a moving composite in relativistic quantum mechanics in many-particle Dirac models. For a manifestly covariant model one can apply the Lorentz transform to go from the rest frame to a…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. Covariant equations for this motion are demonstrated to possess pathological solutions, when treated nonperturbatively in…