Date of this Version
Communications in Mathematical Physics
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.
Nelson, P. C., & Alvarez-Gaumé, L. (1984). Hamiltonian Interpretation of Anomalies. Communications in Mathematical Physics, 99 (1), 103-114. http://dx.doi.org/10.1007/BF01466595
Date Posted: 01 May 2017
This document has been peer reviewed.