Related papers: Least-action principle and path-integral for class…
The Fermat principle indicates that light chooses the temporally shortest path. The action for this "motion" is the observed time, and it has no Lorentz invariance. In this paper we show how this action can be obtained from relativistic…
The article proposes generalizations of the macroscopic model of plasma of scalar charged particles to the cases of inter-particle interaction with multiple scalar fields and negative effective masses of these particles. The model is based…
A least action principle for damping motion has been previously proposed with a Hamiltonian and a Lagrangian containing the energy dissipated by friction. Due to the space-time nonlocality of the Lagrangian, mathematical uncertainties…
The principle of least action seems not to lead to equations describing the motion consistent with the physical behaviour, for non-holonomic constraints. Here, a response is proposed for this fundamental problem in Mathematical Physics.…
We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…
It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some…
The classical Lagrange formalism is generalized to the case of arbitrary stationary (but not necessarily conservative) dynamical systems. It is shown that the equations of motion for such systems can be derived in the standard ways from the…
This paper presents a formulation of Noether's theorem for fractional classical fields. We extend the variational formulations for fractional discrete systems to fractional field systems. By applying the variational principle to a…
Starting from the Dirac equation coupled to a classical radiation field a set of equations of motion for charged quasi-particles in the classical limit for slowly varying radiation and matter fields is derived. The radiation reaction term…
The higher derivative gravitational theories exhibit new phenomena absent in General Relativity. One of them is the possible formation of the so called double layer which is the pure gravitational phenomenon and can be interpreted, in a…
We derive the classical dynamics of massless charged particles in a rigorous way from first principles. Since due to ultraviolet divergences this dynamics does not follow from an action principle, we rely on a) Maxwell's equations, b)…
After the justification of the maximum entropy principle for equilibrium mechanical system from the principle of virtual work, i.e., the virtual work of microscopic forces on the elements of a mechanical system vanishes in thermodynamic…
We consider here the coexistence of first- and third-order integrals of motion in two dimensional classical and quantum mechanics. We find explicitly all potentials that admit such integrals, and all their integrals. Quantum superintegrable…
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex…
The formulation of noncommutative quantum mechanics as a quantum system represented in the space of Hilbert-Schmidt operators is used to systematically derive, using the standard time slicing procedure, the path integral action for a…
The construction of effective Lagrangians commonly involves the application of the `classical equation of motion' to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in…
The paper contains description of the path integrals in the action-angle phase space. It allows to split the action and angle degrees of freedom and to show that the angular quantum corrections cancel each other if the classical classical…
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 by a (Hamiltonian) constraint…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
Whereas the entropy of any deterministic classical system described by a principle of least action is zero, one can assign a "quantum information" to quantum mechanical degree of freedom equal to Hausdorff area of the deviation from a…