Geometric Quantization

SpringerBriefs in Mathematics - Hamiltonian Group Actions and Equivariant Cohomology ◽

10.1007/978-3-030-27227-2_11 ◽

2019 ◽

pp. 103-112

Author(s):

Shubham Dwivedi ◽

Jonathan Herman ◽

Lisa C. Jeffrey ◽

Theo van den Hurk

Keyword(s):

Geometric Quantization

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Generalized operator-valuedpq-symbols and geometric quantization

Functional Analysis and Its Applications ◽

10.1007/bf01080015 ◽

1995 ◽

Vol 29 (2) ◽

pp. 133-135 ◽

Cited By ~ 1

Author(s):

A. V. Karabegov

Keyword(s):

Geometric Quantization ◽

Generalized Operator

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Topological field theories on manifolds with Wu structures

Reviews in Mathematical Physics ◽

10.1142/s0129055x17500155 ◽

2017 ◽

Vol 29 (05) ◽

pp. 1750015 ◽

Cited By ~ 6

Author(s):

Samuel Monnier

Keyword(s):

Topological Field Theories ◽

Geometric Quantization ◽

Discrete Symmetry ◽

Local System ◽

Field Theories ◽

Simons Theory ◽

General Point ◽

Topological Field ◽

Generalized Cohomology ◽

Chern Simons

We construct invertible field theories generalizing abelian prequantum spin Chern–Simons theory to manifolds of dimension [Formula: see text] endowed with a Wu structure of degree [Formula: see text]. After analyzing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf–Witten theories. We take a general point of view where the Chern–Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern–Simons action. In the 3-dimensional spin case, the latter provides a definition of the “fermionic correction” introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the state space of the gauged theories, we develop an analogue of geometric quantization for finite abelian groups endowed with a skew-symmetric pairing. The physical motivation for this work comes from the fact that in the [Formula: see text] case, the gauged 7-dimensional topological field theories constructed here are essentially the anomaly field theories of the 6-dimensional conformal field theories with [Formula: see text] supersymmetry, as will be discussed elsewhere.

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Remarks on the geometric quantization of the Kepler problem

Letters in Mathematical Physics ◽

10.1007/bf00398955 ◽

1988 ◽

Vol 16 (3) ◽

pp. 189-197 ◽

Cited By ~ 6

Author(s):

Giuseppe Gaeta ◽

Mauro Spera

Keyword(s):

Kepler Problem ◽

Geometric Quantization

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