Anomalies in finite dimensions

[摘要] A problem in quantum mechanics is finding a determinant function on linear maps between two vector spaces. In this paper we consider the question in the context of finite dimensional vector spaces. Given two finite dimensional complex vector spaces V and W, we let a group act on both V and W and find conditions for the existence of a global or local analytic determinant function that is invariant under conjugation by the group actions. For instance, for the group SU(n) the usual determinant function is invariant under conjugation by any group actions. For the group U(n) the usual determinant function is invariant under conjugation by any irreducible group actions whose $Ssp1$ actions are isomorphic; when they differ, neither a global nor an analytic determinant function can be found.

[发布机构] Rice University