Dimensional expansion for the Ising limit of quantum field theory

Journal Article · Mon Nov 15 04:00:00 EST 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.48.4919· OSTI ID:5948615

Bender, C M; Boettcher, S ^[1]

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1. Department of Physics, Washington University, St. Louis, Missouri 63130 (United States)

A recently proposed technique, called dimensional expansion, uses the space-time dimension [ital D] as an expansion parameter to extract nonperturbative results in quantum field theory. Here we apply dimensional-expansion methods to examine the Ising limit of a self-interacting scalar field theory. We compute the first few coefficients in the dimensional expansion of [gamma][sub 2[ital n]], the renormalized 2[ital n]-point Green's function at zero momentum, for [ital n]=2, 3, 4, and 5. Because the exact results for [gamma][sub 2[ital n]] are known at [ital D]=1 we can compare the predictions of the dimensional expansion at this value of [ital D]. We find typical accuracies of less than 5%. The radius of convergence of the dimensional expansion for [gamma][sub 2[ital n]] appears to be 2[ital n]/([ital n][minus]1). As a function of the space-time dimension [ital D], [gamma][sub 2[ital n]] appears to rise monotonically with increasing [ital D] and we conjecture that it becomes infinite at [ital D]=2[ital n]/([ital n][minus]1). We presume that for values of [ital D] greater than this critical value [gamma][sub 2[ital n]] vanishes identically because the corresponding [phi][sup 2[ital n]] scalar quantum field theory is free for [ital D][gt]2[ital n]/([ital n][minus]1).

• OSTI ID: 5948615
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 48:10; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONVERGENCE
DIMENSIONS
EXPANSION
FIELD THEORIES
FUNCTIONS
GREEN FUNCTION
QUANTUM FIELD THEORY
SCALAR FIELDS
SPACE-TIME