Related papers: A coherent-state-based path integral for quantum m…

The existence of an observer independent minimum length scale can lead to the modification of the Heisenberg uncertainty principle to the generalized uncertainty principle. This in turn would be responsible for the modification of the…

We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…

We introduce, for the first time, bicoherent-state path integration as a method for quantizing non-hermitian systems. Bicoherent-state path integrals arise as a natural generalization of ordinary coherent-state path integrals, familiar from…

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 address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner transform…

We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…

The formulation of noncommutative quantum mechanics as a quantum system represented in the space of Hilbert-Schmidt operators is used to systematically derive, using the standard time slicing procedure, the path integral action for a…

Four formulations of quantum mechanics on noncommutative Moyal phase spaces are reviewed. These are the canonical, path-integral, Weyl-Wigner and systematic formulations. Although all these formulations represent quantum mechanics on a…

We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…

In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given…

We propose an approach based on a generalized quantum mechanics to deal with the basic features of the intrinsic spin Hall effect. This can be done by considering two decoupled harmonic oscillators on the noncommutative plane and evaluating…

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…

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…

In this lecture a short introduction is given into the theory of the Feynman path integral in quantum mechanics. The general formulation in Riemann spaces will be given based on the Weyl- ordering prescription, respectively product ordering…

Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…

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…

A kink-based expression for the canonical partition function is developed using Feynman's path integral formulation of quantum mechanics and a discrete basis set. The approach is exact for a complete set of states. The method is tested on…

We study quantisation of noncommutative gravity theories in two dimensions (with noncommutativity defined by the Moyal star product). We show that in the case of noncommutative Jackiw-Teitelboim gravity the path integral over gravitational…

Applicability of Feynman path integral approach to numerical simulations of quantum dynamics in real time domain is examined. Coherent quantum dynamics is demonstrated with one dimensional test cases (quantum dot models) and performance of…

Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position…