Continuum regulation of the strong-coupling expansion for quantum field theory

Journal Article · Sun Nov 15 04:00:00 EST 1981 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.24.2693· OSTI ID:5944054

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

We study two continuum methods of regulating the formal strong-coupling expansion of the Green's functions, obtained by expanding the path integral in powers of the kinetic energy (inverse free propagator). Our continuum regulations amount to introducing either a hard (theta function) or soft (Gaussian) cutoff ..lambda.. in momentum space. The cutoff takes the place of the usual spatial cutoff, the lattice spacing, which arises when the path integral is defined as the continuum limit of ordinary integrals on a Euclidean space-time lattice. We find, by investigating free field theory and gphi/sup 4/ field theory in one dimension, that the theta-function regulation is more accurate than the Gaussian and, unlike the Gaussian, preserves certain continuum Green's function identities. The extension to field theories with fermions is trivial and we give the strong-coupling graphical rules for an arbitrary field theory with fermions and bosons in d dimensions.

• Research Organization: Washington University, St. Louis, Missouri 63130
• OSTI ID: 5944054
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 24:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645204* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties
645400 -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
EUCLIDEAN SPACE
FERMIONS
FEYNMAN PATH INTEGRAL
FIELD THEORIES
FUNCTIONS
GREEN FUNCTION
INTEGRALS
LAGRANGIAN FUNCTION
MATHEMATICAL MODELS
MATHEMATICAL SPACE
PARTICLE MODELS
PAULI PRINCIPLE
PHI4-FIELD THEORY
PROPAGATOR
QUANTUM FIELD THEORY
RIEMANN SPACE
SPACE
SPACE-TIME
STRONG-COUPLING MODEL