Related papers: Path Integration in Conical Space
The Einstein action for the gravitational field has some properties which make of it, after quantization, a rare prototype of systems with quantum configurations that do not have a classical analogue. Assuming spherical symmetry in order to…
The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac…
We derive a path integral expression for the transition amplitude in 1+1-dimensional QCD starting from canonically quantized QCD. Gauge fixing after quantization leads to a formulation in terms of gauge invariant but curvilinear variables.…
Free scalar field theory on a flat spacetime can be cast into a generally covariant form known as parametrised field theory in which the action is a functional of the scalar field as well as the embedding variables which describe arbitrary,…
In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum…
We investigate the effect of curvature on the behaviour of a quantum particle bound to move on a surface. For the Gaussian bump we derive and discuss the quantum potential which results in the appearance of a bound state for particles with…
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.
Path integrals constitute powerful representations for both quantum and stochastic dynamics. Yet despite many decades of intensive studies, there is no consensus on how to formulate them for dynamics in curved space, or how to make them…
A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…
We describe how to construct and compute unambiguously path integrals for particles moving in a curved space, and how these path integrals can be used to calculate Feynman graphs and effective actions for various quantum field theories with…
The aim of the article is to show how a coordinate transformation can be applied to the path-integral formalism. For this purpose the unitary definition of the quantum measure, which guarantees the conservation of total probability, is…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
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…
The motion of quantum particles homogeneously constrained to a curved surface is affected by a curvature induced geometric potential. Here, we consider the case of inhomogeneous confinement and derive the effective Hamiltonian by extending…
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
The Euclidean path integral is compared to the thermal (canonical) partition function in curved static space-times. It is shown that if spatial sections are non-compact and there is no Killing horizon, the logarithms of these two quantities…
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…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…