Geometric Quantization in Action

Hurt, Norman E.

doi:10.1007/978-94-009-6963-6

Cited by 132 publications

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“…The relevance of the Fock space and the reproducing aspect of this kernel to the theory of theta functions was revealed by Cartier [2] and Satake [11] and (implicitly, earlier) by Weil [15]. See also Hurt [6], Chapter 8.…”

Section: Resultsmentioning

confidence: 99%

On the dimension of the space of theta functions

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Pekker

2002

Proc. Amer. Math. Soc.

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Abstract. We compute the dimension of the space of theta functions of a given type using a variant of the Selberg trace formula. Main ResultTheta functions play an important role in the theory of abelian varieties; for instance, theta functions are used to construct meromorphic functions on a multidimensional torus and to embed a multidimensional torus into projective space (see, for instance, [8] We imitate Eichler and Selberg in constructing an automorphic reproducing kernel for theta functions by averaging the Bergman kernel function on the Fock space, and we recover Frobenius' dimension formula by computing the trace of this reproducing kernel.Let Λ be a lattice in C n (i.e., Λ is a Z-module of dimension 2n). A theta function of (L, M ) type on C n with respect to Λ is a meromorphic function, not identically

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Section: Resultsmentioning

confidence: 99%

On the dimension of the space of theta functions

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Pekker

2002

Proc. Amer. Math. Soc.

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“…Without Belavin-Knizhnik theorem the Polyakov string measures could be discussed in terms of either Shottky parametrization [9] or Selberg traces [10]. With this theorem the adequate language became that of the Mumford measure dµ on the moduli space of complex curves (= Riemann surfaces) [11,12]: the measure for bosonic string was proved in [3] to be |dµ| 2 det(Im T ) 13 , while that for the NSR superstring [13] had to contain an extra factor of (det (Im T )) 8 with dµ presumably multiplied by some modular form of the weight 8.…”

Section: Jhep05(2008)086mentioning

confidence: 99%

NSR superstring measures revisited

Morozov¹

2008

J. High Energy Phys.

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“…This constructive formulation lead to more drastic and deeper understanding of ghost fields, gauge fixing, and eventually BRST transformations in terms of symplectic geometry. Such geometric method of quantization of gauge theories based on symplectic data is conventionally referred to as geometric BRST quantization [45][46][47].…”

Section: Introductionmentioning

confidence: 99%