Related papers: Path Integrals in Noncommutative Quantum Mechanics
The Feynman path integral approach to quantum mechanics is examined in the case where the configuration space is curved. It is shown how the ambiguity that is present in the choice of path integral measure may be resolved if, in addition to…
By considering the most general metric which can occur on a contractable two dimensional symplectic manifold, we find the most general Hamiltonians on a two dimensional phase space to which equivariant localization formulas for the…
We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
We consider a simple modification of standard phase-space path integrals and show that it leads in configuration space to Lagrangians depending also on accelerations.
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a non-relativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical…
It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…
I consider the case of two interacting scalar fields, \phi and \psi, and use the path integral formalism in order to treat the first classically and the second quantum-mechanically. I derive the Feynman rules and the resulting equation of…
In this work, we study the Quantum Field Theory version of the higher derivative Pais-Uhlenbeck oscillator. We quantize canonically this system and construct its Fock space, as well as study its path integral. We demonstrate that the…
Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In…
We study the Caldeira-Leggett model where a quantum Brownian particle interacts with an environment or a bath consisting of a collection of harmonic oscillators in the path integral formalism. Compared to the contours that the paths take in…
Certain phase space path integrals can be evaluated exactly using equivariant cohomology and localization in the canonical loop space. Here we extend this to a general class of models. We consider hamiltonians which are {\it a priori}…
We develop simple rules for performing integrals over products of distributions in coordinate space. Such products occur in perturbation expansions of path integrals in curvilinear coordinates, where the interactions contain terms of the…
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermitian operator. Contrary to the case of purely scalar…
We present a computation of the coherent state path integral for a generic linear system using ``functional methods'' (as opposed to discrete time approaches). The Gaussian phase space path integral is formally given by a determinant built…
A path-integral approach to quantum acoustics is developed here. In contrast to the commonly utilized particle perspective, this emerging field brings forth a long neglected but essential wave paradigm for lattice vibrations. Within the…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
We present a new formulation for the emergence of classical dynamics in a quantum world by considering a path integral approach that also incorporates continuous measurements. Our program is conceptually different from the decoherence…
It is known that actions of field theories on a noncommutative space-time can be written as some modified (we call them $\theta$-modified) classical actions already on the commutative space-time (introducing a star product). Then the…