These notes are based on lectures that I gave at the Summer School in Mathematical
Analysis at the Instituto de Matem aticas de la Universidad Nacional Aut onoma de M exico …

This paper surveys developments over the last decade in harmonic analysis on Lie groups
relative to a heat kernel measure. These include analogs of the Hermite expansion, the …

Let K be a connected Lie group of compact type and let T*(K) be its cotangent bundle. This
paper considers geometric quantization of T*(K), first using the vertical polarization and then …

We study the Segal–Bargmann transform on a symmetric space X of compact type, mapping
L2 (X) into holomorphic functions on the complexification XC. We invert this transform by …

We describe a family of coherent states and an associated resolution of the identity for a
quantum particle whose classical configuration space is the d-dimensional sphere S d. The …

Let K be a compact, connected Lie group and K_C its complexification. I consider the Hilbert
space HL^2\left(K_C,ν_t\right) of holomorphic functions introduced in H1, where the …

We study phase space properties of critical, parity symmetric, N-qudit systems undergoing a
quantum phase transition (QPT) in the thermodynamic N→∞ limit. The D= 3 level (qutrit) …

This is the second paper concerning gauge-invariant coherent states for loop quantum
gravity. Here, we deal with the gauge group SU (2), this being a significant complication …

We use a variant of the Segal–Bargmann transform to study canonically quantized Yang–
Mills theory on a space-time cylinder with a compact structure group K. The non-existent …

The heat kernel transform Ht is studied for the Heisenberg group in detail. The main result
shows that the image of Ht is a direct sum of two weighted Bergman spaces, in contrast to …