Related papers: Phase-space Quantization of Field Theory
A complete solution to the problem of setting up Wigner distribution for N-level quantum systems is presented. The scheme makes use of some of the ideas introduced by Dirac in the course of defining functions of noncommuting observables and…
The deformation quantization formalism is applied to the linearized gravitational field. Standard aspects of this formalism are worked out before the ground state Wigner functional is obtained. Finally, the propagator for the graviton is…
We describe the symplectic reduction construction for the physical phase space in gauge theory and apply it for the BF theory. Symplectic reduction theorem allows us to rewrite the same phase space as a quotient by the gauge group action,…
Phase-space features of the Wigner flow are examined so to provide a set of continuity equations that describe the flux of quantum information in the phase-space. The reported results suggest that the non-classicality profile of anharmonic…
We define a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum. The distribution function is thus defined on discrete…
The canonical quantization in Weyl gauge of gauge fields in static space-times is presented. With an appropriate definition of transverse and longitudinal components of gauge fields, the Gauss law constraint is resolved explicitly for…
Starting from Feynman's Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
In this note we review the concept of phase space in classical field theory, discussing several variations on the basic notion, as well as the relation between them. In particular we will focus on the case where the field theory admits…
The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group $G$ is developed in detail. Several New features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion…
A classical theorem of Stone and von Neumann says that the Schr\"{o}dinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on…
Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the…
We reformulate time evolution of systems in mixed states in terms of the classical observables of correlators using the Weyl correspondence rule. The resulting equation of motion for the Wigner functional of the density matrix is found to…
The effects of interpreting classical phase space distributions as Wigner functions, which is common in models of multiparticle production, are discussed. The temperature for the classical description is always higher than that for its…
The quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
A gauge-invariant Wigner quasi-distribution function for charged particles in classical electromagnetic fields is derived in a rigorous way. Its relation to the axial gauge is discussed, as well as the relation between the kinetic and…
Interesting non-linear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator valued distributions. Therefore, one is usually forced to find a…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
Starting from the equation of motion of the quantum operator of a real scalar field phi in de Sitter space-time, a simple differential equation is derived which describes the evolution of quantum fluctuations <phi^2> of this field. Full de…