Hamiltonian Interpretation of Anomalies

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. Disciplines Physical Sciences and Mathematics | Physics 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. This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/566