Related papers: Least-action principle and path-integral for class…
It is known that one can construct non-parametric functions by assuming classical axioms. Our work is a converse to that: we prove classical axioms in dependent type theory assuming specific instances of non-parametricity. We also address…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
This paper provides a derivation of Zipf-Pareto laws directly from the principle of least effort. A probabilistic functional of efficiency is introduced as the consequence of an extension of the nonadditivity of the efficiency of…
The search of the correct equation of motion for a classical charged particle under the action of its electromagnetic (EM) self-field, the so-called \textit{radiation-reaction equation of motion}, remains elusive to date. In this paper we…
A natural mapping of paths in a curved space onto the paths in the corresponding (tangent) flat space may be used to reduce the curved-space-time path integral to the flat-space-time path integral. The dynamics of the particle in a curved…
Infinitesimal variation of Action functional in classical (non-quantum) field theory with higher derivatives is presented in terms of well-defined intrinsic geometric objects independent of the particular field which varies. 'Integration by…
The motion equation with nonzero mass, invariant for weak isospin transformation, can be obtained from the Dirac equation by the adding of the Clifford pentad fifth element. The motion equation of the SU(2) Yang-Mills field components is…
The goal of this article is to investigate the dynamics of semi-relativistic or non-relativistic charged particles in interaction with a scalar meson field. Our main contribution is the derivation of the classical dynamics of a…
This paper follows in the tradition of direct-action versions of electromagnetism having the aim of avoiding a balance of infinities wherein a mechanical mass offsets an infinite electromagnetic mass so as to arrive at a finite observed…
The aim of the present article is to construct quadratically integrable three dimensional systems in non-vanishing magnetic fields which possess so-called non-subgroup type integrals. The presence of such integrals means that the system…
Semiclassical methods are extremely valuable in the study of transport and thermodynamical properties of ballistic microstructures. By expressing the conductance in terms of classical trajectories, we demonstrate that quantum interference…
We derive the semiclassical series for the partition function of a one-dimensional quantum-mechanical system consisting of a particle in a single-well potential. We do this by applying the method of steepest descent to the path-integral…
We re-consider the procedure of ``taking a square root of the Dirac equation'' on the superspace and show that it leads to the well known superfield W_\alpha and to the proper equations of motion for the components, i.e. the Maxwell…
We explore the relation between the quantum and semiclassical instanton approximations for the reaction rate constant. From the quantum instanton expression, we analyze the contributions to the rate constant in terms of minimum-action paths…
In this paper we study the non-relativistic dynamic of a charged particle in the electromagnetic field induced by a periodically time dependent current J along an infinitely long and infinitely thin straight wire. The motions are described…
We derive the semiclassical approximation to Feynman's path integral representation of the energy Green function of a massless particle in the shadow region of an ideal obstacle in a medium. The wavelength of the particle is assumed to be…
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities…
We show the value of mass-momentum diagrams for analyzing collision problems in classical mechanics in one dimension. Collisions are characterized by the coefficient of restitution and the momentum of the interacting particles both before…
New method of quantization is presented. It is based on classical Newton-Lagrange equations of motion (representing the fundamental physical law of mechanics) rather than on their traditional Lagrangian and/or Hamiltonian precursors. It is…