Accelerating the loop expansion

Technical Report · Tue Jul 29 04:00:00 EDT 1986

DOI:https://doi.org/10.2172/6982668· OSTI ID:6982668

Ingermanson, R

This thesis introduces a new non-perturbative technique into quantum field theory. To illustrate the method, I analyze the much-studied phi/sup 4/ theory in two dimensions. As a prelude, I first show that the Hartree approximation is easy to obtain from the calculation of the one-loop effective potential by a simple modification of the propagator that does not affect the perturbative renormalization procedure. A further modification then susggests itself, which has the same nice property, and which automatically yields a convex effective potential. I then show that both of these modifications extend naturally to higher orders in the derivative expansion of the effective action and to higher orders in the loop-expansion. The net effect is to re-sum the perturbation series for the effective action as a systematic ''accelerated'' non-perturbative expansion. Each term in the accelerated expansion corresponds to an infinite number of terms in the original series. Each term can be computed explicitly, albeit numerically. Many numerical graphs of the various approximations to the first two terms in the derivative expansion are given. I discuss the reliability of the results and the problem of spontaneous symmetry-breaking, as well as some potential applications to more interesting field theories. 40 refs.

• Research Organization: Lawrence Berkeley Lab., CA (USA); California Univ., Berkeley (USA). Dept. of Physics
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 6982668
• Report Number(s): LBL-21916; ON: DE87002569
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACTION INTEGRAL
FIELD THEORIES
HARTREE-FOCK METHOD
INTEGRALS
LATTICE FIELD THEORY
PERTURBATION THEORY
PHI4-FIELD THEORY
QUANTUM FIELD THEORY
SERIES EXPANSION
SYMMETRY BREAKING