Zero modes, boundary conditions and anomalies on the lattice and in the continuum
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.
scientific article; zbMATH DE number 3878035