Strong-coupling expansion in quantum field theory

Journal Article · Thu Mar 15 04:00:00 EST 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.19.1865· OSTI ID:6078400

Bender, C M; Cooper, F; Guralnik, G S; Sharp, D H

We derive a simple and general diagrammatic procedure for obtaining the strong-coupling expansion of a d-dimensional quantum field theory, starting from its Euclidean path-integral representation. At intermediate stages we are required to evaluate diagrams on a lattice; the lattice spacing provides a cutoff for the theory. We formulate a simple Pade-type prescription for extrapolating to zero lattice spacing and thereby obtain a series of approximants to the true strong-coupling expansion of the theory. No infinite quantities appear at any stage of the calculation. Moreover, all diagrams are simple to evaluate (unlike the diagrams of the ordinary weak-coupling expansion) because nothing more than algebra is required, and no diagram, no matter how complex, generates any transcendental quantities. We explain our approach in the context of a gphi/sup 4/ field theory and calculate the two-point and four-point Green's functions. Then we specialize to d = 1 (the anharmonic oscillator) and compare the locations of the poles of the Green's functions with the tabulated numerical values of the energy levels. The agreement is excellent. Finally, we discuss the application of these techniques to other models such as gphi/sup 2N/, g (psi-barpsi)/sup 2/, and quantum electrodynamics.

• Research Organization: Department of Physics, Washington University, St. Louis, Missouri 63130
• OSTI ID: 6078400
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 19:6; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COUPLING CONSTANTS
ELECTRODYNAMICS
ENERGY LEVELS
FEYNMAN PATH INTEGRAL
FIELD THEORIES
FUNCTIONS
GREEN FUNCTION
INTEGRALS
MATHEMATICAL MODELS
PARTICLE MODELS
PHI4-FIELD THEORY
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
SPACE-TIME
STRONG-COUPLING MODEL