相关论文: Feynman Path Integral on the Noncommutative Plane

Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which…

We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…

These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…

The transition amplitude is obtained for a free massive particle of arbitrary spin by calculating the path integral in the index-spinor formulation within the BFV-BRST approach. None renormalizations of the path integral measure were…

The concepts of Feynman integrals in white noise analysis are used to construct the Feynman integrand for the harmonic oscillator in momentum space representation as a Hida distribution. Moreover it is shown that in a limit sense, the…

The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…

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 action for a relativistic free particle of mass m receives a contribution $-m R(x,y)$ from a path of length R(x,y) connecting the events $x^i$ and $y^i$. Using this action in a path integral, one can obtain the Feynman propagator for a…

We employ the path integral approach developed in [29] to discuss the (generalized) harmonic oscillator in a noncommutative plane. The action for this system is derived in the coherent state basis with additional degrees of freedom. From…

A calculation is presented that shows that Feynman's path integral implies Ostrogradsky's Hamiltonian for nonsingular Lagrangians with second derivatives. The procedure employs the stationary phase approximation to obtain the limiting…

We study the convergence in $L^2$ of the time slicing approximation of Feynman path integrals under low regularity assumptions on the potential. Inspired by the custom in Physics and Chemistry, the approximate propagators considered here…

In this paper, we have constructed the Feynman path integral method for non-paraxial optics. This is done by using the mathematical analogy between a non-paraxial optical system and the generalized Schr\"odinger equation deformed by the…

When path integrals are discussed in quantum field theory, it is almost always assumed that the fields take values in a vector bundle. When the fields are instead valued in a possibly-curved fiber bundle, the independence of the formal path…

The concepts of phase space Feynman integrals in White Noise Analysis are established. As an example the harmonic oscillator is treated. The approach perfectly reproduces the right physics. I.e., solutions to the Schr\"odinger equation are…

In order to evaluate the Feynman path integral in noncommutative quantum mechanics, we consider properties of a Lagrangian related to a quadratic Hamiltonian with noncommutative spatial coordinates. A quantum-mechanical system with…

In this paper we introduce a new procedure on precise analysis of various physical manifestations in superconducting Qubits using the concept of Feynman path integral in quantum mechanics and quantum field theory. Three specific problem are…

As an alternative but unified and more fundamental description for quantum physics, Feynman path integrals generalize the classical action principle to a probabilistic perspective, under which the physical observables' estimation translates…

This paper describes the use of Feynman photon path integrals to compute the probability of detecting reflected, diffracted, and scattered photons at different points in space after interacting with conduction electrons. Five examples are…

We construct a quantum theory of light in nonlinear dielectric media with dispersion and absorption. We employ a mesoscopic model for the light-matter interaction that include a fourth-order nonlinearity in the material response.…

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…