Geometrical Quantization in Fock Space

Details Geometrical Quantization in Fock Space Geometrical Quantization in Fock Space

1995-12-09

arxiv.org/abs/q-alg/9512012v1

Mathematics

Quantum Algebra

34 pages, LaTeX, no figures, to appear in Advances in Soviet Mathematics, a Berezin memorial volume

Scientific paper

We investigate an infinite dimensional analog of the theory of Lagrangian manifolds with complex germs. To such a manifold we assign a canonical operator that depends on creation and annihilation operators. This operator is by definition the geometrical quantization for these isotropic manifolds with complex germs. We prove that for secondary quantized equations this quantization is the asymptotics for the Cauchy problem. Results of Berezin are used thouroughly in the construction of the canonical operator and in proofs of the theorems.

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