Renormalizing the strong-coupling expansion for quantum field theory: present status

Conference · Tue Jan 01 04:00:00 EST 1980

OSTI ID:5483808

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

Progress made in determining the renormalized strong coupling expansion in quantum field theory is reviewed. Consideration restricted is to lambda phi/sup 4/ field theory in d dimensions. The starting point is the lattice version of the path integral representation for the Green's functions. The unrenormalized strong coupling expansion on the lattice is determined first. This is a series in a dimensionless parameter, x. A simple set of graphical rules for determining the Green's functions of the theory in a power series in x is derived. For finite field theories (d < 2) scheme for extrapolating to zero lattice spacing (a ..-->.. 0) is presented. This scheme determines a sequence of approximants to the unrenormalized strong coupling series in the form of a series. Then the problem of renormalization is considered. For the lattice field theory this consists of eliminating x in favor of y, a renormalized x. For d < 2, M/sub R//sup 2/ = 0 occurs when M/sub 0//sup 2/ ..-->.. - infinity, where M/sub R/ is the renormalized mass and M/sub 0/ is the bare mass, and thus the path integral is dominated by instantons. The renormalized strong coupling expansion is valid for the double well where M/sub R//sup 2/ << lambda/sup 2/(4-d)/. The renormalized strong coupling expansion is obtained by two methods. The extrapolation procedure for obtaining the continuum limit of the renormalized lattice field theory works well in zero, one and two dimensions when compared with the exact instanton results. 2 figures, 1 table. (RWR)

• Research Organization: Los Alamos Scientific Lab., NM (USA)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 5483808
• Report Number(s): LA-UR-80-482; CONF-800123-2
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DOCUMENT TYPES
FEYNMAN PATH INTEGRAL
FIELD THEORIES
FUNCTIONS
GREEN FUNCTION
INTEGRALS
LATTICE FIELD THEORY
MATHEMATICAL MODELS
PARTICLE MODELS
PHI4-FIELD THEORY
POWER SERIES
QUANTUM FIELD THEORY
RENORMALIZATION
REVIEWS
SERIES EXPANSION
STRONG-COUPLING MODEL