nLab Bargmann-Fock space

Idea

The Bargmann–Fock space (also Bargmann-Segal space or Segal–Bargmann space) is a Hilbert space of complex analytic functions with certain growth conditions.

Related concepts

• coherent state

• Bargmann-Segal transform

Literature

• Wikipedia, Bargmann space

The original reference is

• Valentine Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Communications on Pure and Applied Mathematics 14 (1961) 187-214 [doi:10.1002/cpa.3160140303)MR0157250]

A generalization

• M. Arik, D. D. Coon, Hilbert spaces of analytic functions and generalized coherent states, J. Math. Phys. 17, 524–527 (1976) doi