Coherent representation of fields and deformation quantization

Abstract

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 scalar field within the deformation quantization program. Notably, the symbol of a symmetric ordered operator in terms of holomorphic variables may be straightforwardly obtained by the quantum field analogue of the Husimi distribution associated with a normal ordered operator. This relation also allows establishing a $c$-equivalence between the Moyal and the normal star-products. In addition, by writing the density operator in terms of coherent states we are able to directly introduce a series representation of the Wigner functional distribution which may be convenient in order to calculate probability distributions of quantum field observables without performing formal phase space integrals at all.

arXiv comment18 pages, no figures

References in corpus (16)

• Deformation quantization of Poisson manifolds, I
• An introduction to the tomographic picture of quantum mechanics
• Deformation quantization in the teaching of quantum mechanics
• Generalized Coherent State Approach to Star Products and Applications to the Fuzzy Sphere
• Deformation quantization of cosmological models
• Star products and perturbative quantum field theory
• Deformation Quantization of Classical Fields
• On the Schroedinger Representation for a Scalar Field on Curved Spacetime
• Matrix Bases for Star Products: a Review
• Polymer Quantum Mechanics as a Deformation Quantization
• Locally Noncommutative Space-Times
• The Polymer representation for the scalar field: A Wigner functional approach
• Characteristic classes of star products on Marsden-Weinstein reduced symplectic manifolds
• Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective
• Deformation quantization of constrained systems: a group averaging approach
• Integral representations of the star product corresponding to the $s$-ordering of the creation and annihilation operators

Cited by in corpus (3)

• Wigner functional theory for quantum optics
• Fermion quadrature bases for Wigner functionals
• Quantization due to the time evolution, with applications to Quantum Yang-Mills theory, Quantum Gravity and Classical Statistical Field Theory