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Title: Questionable and unquestionable in the perturbation theory of non-Abelian models

Abstract

We show, by explicit computation, that bare lattice perturbation theory in the two-dimensional O(n) nonlinear {sigma} models with superinstanton boundary conditions is divergent in the limit of an infinite number of points {vert_bar}{Lambda}{vert_bar}. This is the analogue of David{close_quote}s statement that renormalized perturbation theory of these models is infrared divergent in the limit where the physical size of the box tends to infinity. We also give arguments which support the validity of the bare perturbative expansion of short-distance quantities obtained by taking the limit {vert_bar}{Lambda}{vert_bar}{r_arrow}{infinity} term by term in the theory with more conventional boundary conditions such as Dirichlet, periodic, and free. {copyright} {ital 1997} {ital The American Physical Society}

Authors:
 [1]; ;  [2]
  1. Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland)
  2. Max-Planck-Institut fuer Physik, Foehringer Ring 6, D-80805 Muenchen (Germany)
Publication Date:
OSTI Identifier:
538692
Resource Type:
Journal Article
Journal Name:
Physical Review, D
Additional Journal Information:
Journal Volume: 56; Journal Issue: 5; Other Information: PBD: Sep 1997
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; PERTURBATION THEORY; SIGMA MODEL; LATTICE FIELD THEORY; INSTANTONS; NONLINEAR PROBLEMS; RENORMALIZATION; BOUNDARY CONDITIONS; O GROUPS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Niedermayer, F, Niedermaier, M, and Weisz, P. Questionable and unquestionable in the perturbation theory of non-Abelian models. United States: N. p., 1997. Web. doi:10.1103/PhysRevD.56.2555.
Niedermayer, F, Niedermaier, M, & Weisz, P. Questionable and unquestionable in the perturbation theory of non-Abelian models. United States. https://doi.org/10.1103/PhysRevD.56.2555
Niedermayer, F, Niedermaier, M, and Weisz, P. 1997. "Questionable and unquestionable in the perturbation theory of non-Abelian models". United States. https://doi.org/10.1103/PhysRevD.56.2555.
@article{osti_538692,
title = {Questionable and unquestionable in the perturbation theory of non-Abelian models},
author = {Niedermayer, F and Niedermaier, M and Weisz, P},
abstractNote = {We show, by explicit computation, that bare lattice perturbation theory in the two-dimensional O(n) nonlinear {sigma} models with superinstanton boundary conditions is divergent in the limit of an infinite number of points {vert_bar}{Lambda}{vert_bar}. This is the analogue of David{close_quote}s statement that renormalized perturbation theory of these models is infrared divergent in the limit where the physical size of the box tends to infinity. We also give arguments which support the validity of the bare perturbative expansion of short-distance quantities obtained by taking the limit {vert_bar}{Lambda}{vert_bar}{r_arrow}{infinity} term by term in the theory with more conventional boundary conditions such as Dirichlet, periodic, and free. {copyright} {ital 1997} {ital The American Physical Society}},
doi = {10.1103/PhysRevD.56.2555},
url = {https://www.osti.gov/biblio/538692}, journal = {Physical Review, D},
number = 5,
volume = 56,
place = {United States},
year = {Mon Sep 01 00:00:00 EDT 1997},
month = {Mon Sep 01 00:00:00 EDT 1997}
}