Questionable and unquestionable in the perturbation theory of non-Abelian models
- Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland)
- Max-Planck-Institut fuer Physik, Foehringer Ring 6, D-80805 Muenchen (Germany)
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}
- OSTI ID:
- 538692
- Journal Information:
- Physical Review, D, Vol. 56, Issue 5; Other Information: PBD: Sep 1997
- Country of Publication:
- United States
- Language:
- English
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