Department of Physics Papers

Document Type

Journal Article

Date of this Version

1-1984

Publication Source

Communications in Mathematical Physics

Volume

99

Issue

1

Start Page

103

Last Page

114

DOI

10.1007/BF01466595

Abstract

A family of quantum systems parametrized by the points of a compact space can realizeits classical symmetries via a new kind of nontrivial ray representation. We show that thisphenomenon in fact occurs for the quantum mechanics of fermions in the presence ofbackground gauge fields, and is responsible for both the nonabelian anomaly and Witten’sSU(2) anomaly. This provides a hamiltonian interpretation of anomalies: in the affectedtheories Gauss’ law cannot be implemented. The analysis clearly shows why there are nofurther obstructions corresponding to higher spheres in configuration space, in agreementwith a recent result of Atiyah and Singer.

Comments

At the time of publication, author Philip C. Nelson was affiliated with the Institute for Theoretical Physics at the University of California. Currently, he is a faculty member in the Physics & Astronomy Department at the University of Pennsylvania.

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Date Posted: 01 May 2017

This document has been peer reviewed.