Related papers: Boundary conditions: The path integral approach
A method based on the path integral approach is engaged to consider the gravitational emission from a quantum mechanical bound system in a locally inertial frame. In such a frame, interaction between the electromagnetic (bound potential)…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
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…
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.
Inspired by a recent work that proposes using coherent states to evaluate the Feynman kernel in noncommutative space, we provide an independent formulation of the path-integral approach for quantum mechanics on the Moyal plane, with the…
It is well known that (possibly non-unique) suitable field dynamics can be prescribed in spacetimes with timelike boundaries by means of appropriate boundary conditions. In Ref. [J. Math. Phys. {\bf 21}, 2802 (1980)], Wald derived a…
Boundary conditions strongly affect the results of numerical computations for finite size inhomogeneous or incommensurate structures. We present a method which allows to deal with this problem, both for ground state and for critical…
We describe in detail a physical situation in which instantons are necessarily complex, not just Wick rotations of classical solutions to Euclidean spacetime. These complex instantons arise in the semiclassical evaluation of vacuum pair…
We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is…
In this paper we argue that boundary condition may run with energy scale. As an illustrative example, we consider one-dimensional quantum mechanics for a spinless particle that freely propagates in the bulk yet interacts only at the origin.…
A brief review of some recent results on the global self-adjoint formulation of systems with boundaries is presented. We specialize to the 1-dimensional case and obtain a dynamical formulation of quantum confinement.
For description of the quantum dynamics on a curved group manifold the path integrals in a space of the group parameters is offered. The formalism is illustrated by the $H$-atom problem.
Starting with a quantum particle on a closed manifold without boundary, we consider the process of generating boundaries by modding out by a group action with fixed points, and we study the emergent quantum dynamics on the quotient…
The derivation of path integrals is reconsidered. It is shown that the expression for the discretized action is not unique, and the path integration domain can be deformed so that at least Gaussian path integrals become probabillistic. This…
Quantum dynamics of a particle confined in a box with time-dependent wall is revisited by considering some unexplored aspects of the problem. In particular, the case of dynamical confinement in a time-dependent box in the presence of purely…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work…
Path integrals developed by Richard Feynman have been an important tool in Physics in studying quantum field theory. In mathematics, it has also been widely used in providing formal proofs in the study of Index theorem and asymptotic…
By investigating the Feynman Path Integral we prove that elementary quantum particle dynamics are directly associated to single compact (cyclic) world-line parameters, playing the role of the particles' internal clock, implicit in ordinary…
I assume a universe whereby the speed of light and the planck constant are not constants but instead parameters that vary locally in time-and space. When describing motion, I am able to derive a modified path integral description at the…