nLab coherent state in geometric quantization

Idea

The concept of coherent state in quantum mechanics/quantum physics may be formalized in the context of geometric quantization, The original definition is due to Rawnsley 1977, further developments include Kirwin 2007.

Related concepts

• quantization of Chern-Simons theory

References

The original reference that interpreted coherent states in geometric quantization over Kähler manifolds:

• John H. Rawnsley: Coherent states and Kähler manifolds, Quart. J. Math. Oxford 2 28 (1977) 403-415 [doi:10.1093/qmath/28.4.403]

Review and further developments:

• Mauro Spera, On Kählerian coherent states (djvu)

Generalization to non-Kähler symplectic manifolds is in

• William Kirwin, Coherent states in geometric quantization, J. Geom. Phys. 57 (2007), no. 2, 531–548. arXiv:0502026 MR2008b:53114 doi

See also

• Anatol Odzijewicz, Coherent state method in geometric quantization, in Twenty Years of Bialowiez: a mathematical anthology, Aspects of Differential Geometric Methods in Physics_ (pp 47-78) , World Sci. Monogr. Ser. Math. 8 (2005); Coherent states and geometric quantization, Comm. Math. Phys. 150 (1992), no. 2, 385–413 doi 94c:58077

• Brian Charles Hall, Geometric quantization and the generalized Segal–Bargmann transform for Lie groups of compact type, Comm. Math. Phys., 226:233–268, 2002. doi

• D. J. Rowe, Coherent states, induced representations, geometric quantization, and their vector coherent state extensions, Symmetry in physics, 177–188, CRM Proc. Lecture Notes 34, Amer. Math. Soc. 2004. MR2005a:81100

• C. Florentino, P. Matias, J. Mourão, J. P. Nunes, Geometric quantization, complex structures and the coherent state transform, J. Funct. Anal. 221(2):303–322, 2005 MR2005m:53179 doi