Related papers: Coherent-state path integrals in the continuum via…
The affine coherent states quantization is a promising integral quantization of Hamiltonian systems when the phase space includes at least one conjugate pair of variables which takes values from a half-plane. Such a situation is common for…
Affine variables, which have the virtue of preserving the positive-definite character of matrix-like objects, have been suggested as replacements for the canonical variables of standard quantization schemes, especially in the context of…
The path integral representation of the transition amplitude for a particle moving in curved space has presented unexpected challenges since the introduction of path integrals by Feynman fifty years ago. In this paper we discuss and review…
Although the Hamiltonian formalism is so far favored for quantum computation of lattice gauge theory, the path integral formalism would never be useless. The advantages of the path integral formalism are the knowledge and experience…
Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a…
We introduce an explicit construction for realizing of the space of invariant deformation quantizations on an arbitrary symmetric bounded domain.
Dimerized quantum spin systems may appear under several circumstances, e.g\ by a modulation of the antiferromagnetic exchange coupling in space, or in frustrated quantum antiferromagnets. In general, such systems display a quantum phase…
The Berezin--Simon (BS) quantization is a rigorous version of the ``operator formalism'' of quantization procedure. The goal of the paper is to present a rigorous real-time (not imaginary-time) path-integral formalism corresponding to the…
A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by…
A method of path integral construction without gauge fixing in the holomorphic representation is proposed for finite-dimensional gauge models. This path integral determines a manifestly gauge-invariant kernel of the evolution operator.
The transparent way for the invariant (Hamiltonian) description of equivariant localization of the integrals over phase space is proposed. It uses the odd symplectic structure, constructed over tangent bundle of the phase space and permits…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
For a single degree of freedom confined mechanical system with given energy, we know that the motion is always periodic and action-angle variables are convenient choice as conjugate phase-space variables. We construct action-angle coherent…
A general technique for the periodic orbit quantization of systems with near-integrable to mixed regular-chaotic dynamics is introduced. A small set of periodic orbits is sufficient for the construction of the semiclassical recurrence…
We present a construction of semi-classical states for P\"oschl-Teller potentials based on a supersymmetric quantum mechanics approach. The parameters of these "coherent" states are points in the classical phase space of these systems. They…
Decoherence of a quantum system (which then starts to display classical features) results from the interaction of the system with the environment, and is well described in the framework of the theory of continuous quantum measurements…
Weak coherent states share many properties of the usual coherent states, but do not admit a resolution of unity expressed in terms of a local integral. They arise e.g. in the case that a group acts on an inadmissible fiducial vector.…
The present letter gives a rigorous way from quantum to classical random walks by introducing an independent random fluctuation and then taking expectations based on a path integral approach.
The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough…
A simple, often invoked, regularization scheme of quantum mechanical path integrals in curved space is mode regularization: one expands fields into a Fourier series, performs calculations with only the first $M$ modes, and at the end takes…