Nonunique solution to the Schwinger-Dyson equations

Journal Article · Sat Apr 15 04:00:00 EDT 1989 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.39.2343· OSTI ID:6188213

Bender, C M; Cooper, F; Simmons, Jr, L M

In principle, a path-integral representation for a quantum field theory uniquely determines all of the Green's functions of the theory. One possible way to calculate the Green's functions is to derive from the path-integral representation an infinite set of coupled partial differential equations for the Green's functions known as the Schwinger-Dyson equations. One might think that all nonperturbative information about the Green's functions is contained in the Schwinger-Dyson equations. However, we show that while the Schwinger-Dyson equations do determine the weak-coupling perturbation expansions of the Green's functions, the solution to the Schwinger-Dyson equations is not unique and therefore the nonperturbative content of the Green's functions remains undetermined. In particular, one cannot use the Schwinger-Dyson equations to compute high-temperature or strong-coupling expansions.

• Research Organization: Department of Physics, Washington University, St. Louis, Missouri 63130
• OSTI ID: 6188213
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 39:8; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSON EXPANSION
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
DYSON REPRESENTATION
EQUATIONS
FIELD THEORIES
FOKKER-PLANCK EQUATION
FUNCTIONS
GREEN FUNCTION
MATHEMATICAL MODELS
NUCLEAR MODELS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
QUANTUM FIELD THEORY
SUPERSYMMETRY
SYMMETRY
WARD IDENTITY
WEAK-COUPLING MODEL