相关论文: Path Integral Approach for Superintegrable Potenti…

The problem of a Klein-Gordon particle moving in equal vector and scalar Rosen-Morse-type potentials is solved in the framework of Feynman's path integral approach. Explicit path integration leads to a closed form for the radial Green's…

p-Adic generalization of the Feynman path integrals in quantum mechanics is considered. The probability amplitude for a particle in a constant field is calculated. Path integrals over p-adic space have the same form as those over R.

This paper combines image metamorphosis with deep features. To this end, images are considered as maps into a high-dimensional feature space and a structure-sensitive, anisotropic flow regularization is incorporated in the metamorphosis…

The path-integral representation of Smoluchowski equation is exploited to explore the stochastic dynamics of a tagged Brownian particle within an interacting system where hydrodynamic effects are neglected. In particular, this formalism is…

The path integral representation of the transition amplitude for a particle moving in curved space has presented unexpected challenges since the introduction of path integrals by Feynman fifty years ago. In this paper we discuss and review…

The N-dimensional Hamiltonian H formed by a curved kinetic term (depending on a function f), a central potential (depending on a function U), a Dirac monopole term, and N centrifugal terms is shown to be quasi-maximally superintegrable for…

Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…

In the article the problem of the integrable classification of nonlinear lattices depending on one discrete and two continuous variables is studied. By integrability we mean the presence of reductions of a chain to a system of hyperbolic…

The notion of the integral over the anticommuting Grassmann variables (nonquantum fermionic fields) seems to be the most powerful tool in order to extract the exact analytic solutions for the 2D Ising models on simple and more complicated…

We develop a path integrals approach for analyzing stationary light propagation appropriate for photonic crystals. The hermitian form of the stationary Maxwell equations is transformed into a quantum mechanical problem of a spin 1 particle…

The Feynman path integral of ordinary quantum mechanics is complexified and it is shown that possible integration cycles for this complexified integral are associated with branes in a two-dimensional A-model. This provides a fairly direct…

In this short review paper the detailed analysis of six two-dimensional quantum {\it superintegrable} systems in flat space is presented. It includes the Smorodinsky-Winternitz potentials I-II (the Holt potential), the Fokas-Lagerstrom…

We investigate the hitherto unexplored relation between the superparticle path integral and superfield theory. Requiring that the path integral has the global symmetries of the classical action and obeys the natural composition property of…

We construct a space of ideal elements (particles and their paths) to analyze certain aspects of quantum physics. The particles are taken from a model of particle interaction first described by David Deutsch (based on a different but…

The path integral approach to the quantization of one degree-of-freedom Newtonian particles is considered within the discrete time-slicing approach, as in Feynman's original development. In the time-slicing approximation the quantum…

Quantum information technology is one of the fastest growing sectors within information technology. By misleading interpretations of Bohr's definition of complementarity, the foundation of nonlocal correlations of entanglement is concealed…

We solve numerically exactly a simple toy model to quantum general relativity or more properly to path integral on a curved space. We consider the thermal equilibrium of a quantum many body problem on the sphere, the surface of constant…

Using improper Riemann integrals, we will formulate a rigorous version of the real-time, time-sliced Feynman path integral for the $L^2$ transition probability amplitude. We will do this for nonvector potential Hamiltonians with potential…

The article investigates systems of differential-difference equations of hyperbolic type, integrable in sense of Darboux. The concept of a complete set of independent characteristic integrals underlying Darboux integrability is discussed. A…

We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description…