Operator-product expansion and the asymptotic behavior of spontaneously broken scalar field theories

Journal Article · Thu Sep 15 00:00:00 EDT 1983 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.28.1364· OSTI ID:5810653

Taylor, C; McClain, B

We reexamine a recent study of the operator-product expansion in spontaneously broken scalar field theories. First, the asymptotic behavior of the propagator in a spontaneously broken lambdaphi/sup 4/ theory is calculated to lowest nontrivial order. The use of the operator-product expansion in the ''naive'' vacuum, with operators developing nonvanishing vacuum expectation values, is found to correctly reproduce the usual perturbative analysis of the shifted theory when carried out to the same order. The renormalization-group improvement of this result is studied. We find that ..gamma..2, the renormalization-group coefficient of the operator phi/sup 2/, is nonzero at first order in lambda. This contradicts the result of the study of Gupta and Quinn. The generalization of this analysis to all Green's functions at all orders in perturbation theory is outlined. We argue that the renormalization-group improvement of the perturbation theory should yield the same answer for the two methods of calculating the asymptotic limit. Finally, we discuss the implications of this study for gauge theories.

• Research Organization: Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
• DOE Contract Number: AC02-76ER03069
• OSTI ID: 5810653
• Journal Information: Phys. Rev. D; (United States), Vol. 28:6
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
SCALAR FIELDS
SYMMETRY BREAKING
GAUGE INVARIANCE
GREEN FUNCTION
PERTURBATION THEORY
PHI4-FIELD THEORY
PROPAGATOR
RENORMALIZATION
VACUUM STATES
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
QUANTUM FIELD THEORY
645400* - High Energy Physics- Field Theory
645301 - High Energy Physics- Particle Invariance Principles & Symmetries- General- (-1987)