Coherent States for Compact Lie Groups and Their Large-N Limits

Abstract

The first two parts of this article surveys results related to the heatkernel coherent states for a compact Lie group K. I begin by reviewing the definition of the coherent states, their resolution of the identity, and the associated Segal-Bargmann transform. I then describe related results including connections to geometric quantization and (1 + 1)-dimensional Yang-Mills theory, the associated coherent states on spheres, and applications to quantum gravity.The third part of this article summarizes recent work of mine with Driver and Kemp on the large-N limit of the Segal-Bargmann transform for the unitary group U (N ). A key result is the identification of the leading-order large-N behavior of the Laplacian on "trace polynomials."