nLab
coherent state in geometric quantization

Contents

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 77), further developments include (Kirwin 07).

References

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

  • J. H. Rawnsley, Coherent states and Kähler manifolds, Quart. J. Math. Oxford (2), 28 (1977), pp. 403–415

A review and further developments of these considerations are in

  • Mauro Spera, On Kählerian coherent states (djvu)

Generalization to non-Kähler symplectic manifolds is in

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

Revised on August 29, 2014 10:32:20 by Urs Schreiber (185.37.147.12)