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The perturbative method fails in non-Abelian models

Abstract

It is shown that perturbation theory in 2D nonlinear {sigma}-models as well gauge theories in dimension D{>=}2 produces answers that depend on boundary conditions even after the infinite volume limit has been taken. This unphysical phenomenon occurs only in the non-Abelian versions of those models, starting at O(1/{beta}{sup 2}). It is not present in the true (nonperturbatively defined) models and represents a failure of the perturbative method. It is related to a hitherto unnoticed type of low-lying excitation, dubbed super-instanton, that dominates the low-temperature (= weak coupling) regime of these models. ((orig.)).
Authors:
Patrascioiu, A; [1]  Seiler, E [2] 
  1. Arizona Univ., Tucson, AZ (United States). Dept. of Physics
  2. Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut
Publication Date:
Apr 01, 1995
Product Type:
Journal Article
Report Number:
CONF-9409269-
Reference Number:
SCA: 662110; PA: AIX-26:064348; EDB-95:132471; SN: 95001458363
Resource Relation:
Journal Name: Nuclear Physics B, Proceedings Supplements; Journal Volume: 42; Conference: Lattice `94, Bielefeld (Germany), 25 Sep - 1 Oct 1994; Other Information: PBD: Apr 1995
Subject:
66 PHYSICS; LATTICE FIELD THEORY; PERTURBATION THEORY; SIGMA MODEL; UNIFIED GAUGE MODELS; ASYMPTOTIC SOLUTIONS; BOUNDARY CONDITIONS; EXCITED STATES; INSTANTONS; NONLINEAR PROBLEMS; O GROUPS; QUANTUM ELECTRODYNAMICS; SU-2 GROUPS; TWO-DIMENSIONAL CALCULATIONS; U-1 GROUPS; YANG-MILLS THEORY
OSTI ID:
101041
Country of Origin:
Netherlands
Language:
English
Other Identifying Numbers:
Journal ID: NPBSE7; ISSN 0920-5632; TRN: NL95FF387064348
Submitting Site:
NLN
Size:
pp. 826-828
Announcement Date:
Oct 05, 1995

Citation Formats

Patrascioiu, A, and Seiler, E. The perturbative method fails in non-Abelian models. Netherlands: N. p., 1995. Web. doi:10.1016/0920-5632(95)00393-N.
Patrascioiu, A, & Seiler, E. The perturbative method fails in non-Abelian models. Netherlands. doi:10.1016/0920-5632(95)00393-N.
Patrascioiu, A, and Seiler, E. 1995. "The perturbative method fails in non-Abelian models." Netherlands. doi:10.1016/0920-5632(95)00393-N. https://www.osti.gov/servlets/purl/10.1016/0920-5632(95)00393-N.
@misc{etde_101041,
title = {The perturbative method fails in non-Abelian models}
author = {Patrascioiu, A, and Seiler, E}
abstractNote = {It is shown that perturbation theory in 2D nonlinear {sigma}-models as well gauge theories in dimension D{>=}2 produces answers that depend on boundary conditions even after the infinite volume limit has been taken. This unphysical phenomenon occurs only in the non-Abelian versions of those models, starting at O(1/{beta}{sup 2}). It is not present in the true (nonperturbatively defined) models and represents a failure of the perturbative method. It is related to a hitherto unnoticed type of low-lying excitation, dubbed super-instanton, that dominates the low-temperature (= weak coupling) regime of these models. ((orig.)).}
doi = {10.1016/0920-5632(95)00393-N}
journal = {Nuclear Physics B, Proceedings Supplements}
volume = {42}
journal type = {AC}
place = {Netherlands}
year = {1995}
month = {Apr}
}