Zero modes, boundary conditions and anomalies on the lattice and in the continuum
type: Item
instance of: scholarly article
title: Zero modes, boundary conditions and anomalies on the lattice and in the continuum
zbMATH Open document ID: 0551.58036
DOI: 10.1016/0003-4916(84)90252-5
author: Michael Stone
published in: Annals of Physics
publication date: 1984-01-01T00:00:00Z
review text: The author investigates the relation between the anomalies in the conservation laws, the occurrence of the soft modes and the Atiyah-Singer index theorem in two models where everything can be explicitly computed. The models considered are the one-dimensional polyacetylene and the two- dimensional Kogut-Susskind model. It is shown that in the first case there are exact zero modes but no anomaly, due to the effect of the boundary, and in the second case there is no exact zero mode but the continuum limit has an anomaly. The effect of the boundary leads to an example illustrating the Atiyah-Singer-Patodi theorem.
Mathematics Subject Classification ID: 58J90
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 3878035
zbMATH Keywords: quantum field theory
zbMATH Keywords: lattice models
zbMATH Keywords: anomalies
zbMATH Keywords: conservation laws
zbMATH Keywords: Atiyah-Singer index theorem
zbMATH Keywords: continuum limit
zbMATH Keywords: Atiyah-Singer-Patodi theorem
MaRDI profile type: Publication
full work available at URL: 0003-4916(84)90252-5
OpenAlex ID: W2034592418
cites work: The index of elliptic operators. IV, V
cites work: Spectral asymmetry and Riemannian Geometry. I
cites work: On the Vibrations of Polyatomic Molecules
cites work: Q5790009
cites work: Fermions without spinors
description: scientific article; zbMATH DE number 3878035