Algebraic versus Topologic Anomalies

TL;DR

This paper analyzes algebraic and topological anomalies that occur when translating classical symmetries of Newton equations into quantum theory, illustrating the obstructions with explicit examples.

Contribution

It distinguishes between algebraic and topological anomalies in quantization and provides explicit examples of each type.

Findings

Identifies algebraic and topological obstructions in quantization

Provides explicit examples of each anomaly type

Clarifies the local versus global nature of these anomalies

Abstract

Within the frame of a Group Approach to Quantization anomalies arise in a quite natural way. We present in this talk an analysis of the basic obstructions that can be found when we try to translate symmetries of the Newton equations to the Quantum Theory. They fall into two classes: algebraic and topologic according to the local or global character of the obstruction. We present here one explicit example of each.