Related papers: Least-action principle and path-integral for class…
As is well known, in order for the Einstein--Hilbert action to have a well defined variation, and therefore to be used for deriving field equation through the stationary action principle, it has to be amended by the addition of a suitable…
We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original…
Systems of equations are invariant under "polydimensional transformations" which reshuffle the geometry such that what is a line or a plane is dependent upon the frame of reference. This leads us to propose an extension of Clifford calculus…
We propose an action for the extended sigma - models in the most general setting of the kinetic term allowed in the nontrivially deformed field - antifield formalism. We show that the classical motion equations do naturally take their…
Recently it is shown that the non-relativistic quantum formulations can be derived from a least observability principle [36]. In this paper, we apply the principle to massive scalar fields, and derive the Schr\"{o}dinger equation of the…
The problems of Classical Electrodynamics with the electron equation of motion and with non-integrable singularity of its self-field stress tensor are well known. They are consequences, we show, of neglecting terms that are null off the…
We consider the action principle to derive the classical, non-relativistic motion of a self-interacting particle in a 4-D Lorentzian spacetime containing a wormhole and which allows the existence of closed time-like curves. For the case of…
The paper concerns classical solution of path-dependent partial differential equations (PPDEs) with coefficients depending on both variables of path and path-valued measure, which are crucial to understanding large-scale mean-field…
The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same…
In this paper we analyze perturbatively a g phi^4 classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the…
The classical motion of spinning particles can be described without employing Grassmann variables or Clifford algebras, but simply by generalizing the usual spinless theory. We only assume the invariance with respect to the Poincare' group;…
A dual formalism for Lagrange multipliers is developed. The formalism is used to minimize an action function $S(q_2,q_1,T)$ without any dynamical input other than that $S$ is convex. All the key equations of analytical mechanics -- the…
A mean-field model to describe electron transfer processes in ion-molecule collisions at the $\hbar =0$ level is presented and applied to collisions involving water and ammonia molecules. Multicenter model potentials account for the…
The Maxwell equations in the presence of sources are first derived without making use of the potentials and the Hamilton-Jacobi equation for classical electrodynamics is written down. The manifestly gauge invariant theory is then quantized…
Periodic classical trajectories are of fundamental importance both in classical and quantum physics. Here we develop path integral techniques to investigate such trajectories in an arbitrary, not necessarily energy conserving hamiltonian…
We review various semiclassical models for strong-field physics. These semiclassical models employ ensembles of classical trajectories to simulate electron motion in the continuum after being released from an atom or molecule by an external…
Several relevant aspects of quantum-field processes can be well described by semiclassical methods. In particular, the knowledge of non-trivial classical solutions of the field equations, and the thermal and quantum fluctuations around…
A generalized canonical form of action of dynamic theories with higher derivatives is proposed, which does not require the introduction of additional dynamic variables. This form is the initial point for the construction of quantum theory,…
We present a path-integral formulation of 't Hooft's derivation of quantum from classical physics. The crucial ingredient of this formulation is Gozzi et al.'s supersymmetric path integral of classical mechanics. We quantize explicitly two…
In physics, there is a scalar function called the action which behaves like a cost function. When minimized, it yields the "path of least action" which represents the path a physical system will take through space and time. This function is…