Generalized Wigner functions in curved spaces: A new approach

Journal Article · Fri Apr 15 04:00:00 EDT 1988 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.37.2165· OSTI ID:5124078

Kandrup, H E

It is well known that, given a quantum field in Minkowski space, one can define Wigner functions f/sub W//sup N/(x/sub 1/,p/sub 1/,...,x/sub N/,p/sub N/) which (a) are convenient to analyze since, unlike the field itself, they are c-number quantities and (b) can be interpreted in a limited sense as ''quantum distribution functions.'' Recently, Winter and Calzetta, Habib and Hu have shown one way in which these flat-space Wigner functions can be generalized to a curved-space setting, deriving thereby approximate kinetic equations which make sense ''quasilocally'' for ''short-wavelength modes.'' This paper suggests a completely orthogonal approach for defining curved-space Wigner functions which generalizes instead an object such as the Fourier-transformed f/sub W//sup 1/(k,p), which is effectively a two-point function viewed in terms of the ''natural'' creation and annihilation operators a/sup dagger/(p-(12k) and a(p+(12k). The approach suggested here lacks the precise phase-space interpretation implicit in the approach of Winter or Calzetta, Habib, and Hu, but it is useful in that (a) it is geared to handle any ''natural'' mode decomposition, so that (b) it can facilitate exact calculations at least in certain limits, such as for a source-free linear field in a static spacetime.

• Research Organization: Department of Physics, Syracuse University, Syracuse, New York 13244-1130
• OSTI ID: 5124078
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 37:8; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CLASSICAL MECHANICS
DISTRIBUTION FUNCTIONS
FIELD THEORIES
FOURIER TRANSFORMATION
FUNCTIONS
HAMILTONIANS
INTEGRAL TRANSFORMATIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
MINKOWSKI SPACE
PHASE SPACE
PROBABILITY
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SCALAR FIELDS
SPACE
SPACE-TIME
TRANSFORMATIONS
UNIVERSE
WIGNER DISTRIBUTION