Generalized operator-valuedpq-symbols and geometric quantization

1995 ◽  
Vol 29 (2) ◽  
pp. 133-135 ◽  
Author(s):  
A. V. Karabegov
Keyword(s):  
Geometric Quantization ◽  
Generalized Operator

scholarly journals Topological field theories on manifolds with Wu structures

2017 ◽  
Vol 29 (05) ◽  
pp. 1750015 ◽  
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.

Remarks on the geometric quantization of the Kepler problem

1988 ◽  
Vol 16 (3) ◽  
pp. 189-197 ◽  
Author(s):  
Giuseppe Gaeta ◽  
Mauro Spera
Keyword(s):  
Kepler Problem ◽  
Geometric Quantization

Geometric quantization and constrained systems

1986 ◽  
Vol 27 (5) ◽  
pp. 1319-1330 ◽  
Author(s):  
Abhay Ashtekar ◽  
Matthew Stillerman
Keyword(s):  
Geometric Quantization ◽  
Constrained Systems

Approximate energy eigenvalues from a generalized operator method

1983 ◽  
Vol 95 (9) ◽  
pp. 481-483 ◽  
Author(s):  
Christopher C. Gerry ◽  
Steven Silverman
Keyword(s):  
Operator Method ◽  
Energy Eigenvalues ◽  
Generalized Operator

Generalized Bergman kernels and geometric quantization

1987 ◽  
Vol 28 (3) ◽  
pp. 573-583 ◽  
Author(s):  
G. M. Tuynman
Keyword(s):  
Geometric Quantization ◽  
Bergman Kernels

scholarly journals Generalized collision operator for fast electrons interacting with partially ionized impurities

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
L. Hesslow ◽  
O. Embréus ◽  
M. Hoppe ◽  
T. C. DuBois ◽  
G. Papp ◽  
...  
Keyword(s):  
Growth Rate ◽  
Electric Fields ◽  
Collision Operator ◽  
Impurity Content ◽  
Fast Electrons ◽  
Generalized Operator ◽  
Partially Ionized ◽  
High Electric Fields ◽  
Bound Electrons ◽  
Fokker Planck

Accurate modelling of the interaction between fast electrons and partially ionized atoms is important for evaluating tokamak disruption mitigation schemes based on material injection. This requires accounting for the effect of screening of the impurity nuclei by the cloud of bound electrons. In this paper, we generalize the Fokker–Planck operator in a fully ionized plasma by accounting for the effect of screening. We detail the derivation of this generalized operator, and calculate the effective ion length scales, needed in the components of the collision operator, for a number of ion species commonly appearing in fusion experiments. We show that for high electric fields, the secondary runaway growth rate can be substantially larger than in a fully ionized plasma with the same effective charge, although the growth rate is significantly reduced at near-critical electric fields. Furthermore, by comparison with the Boltzmann collision operator, we show that the Fokker–Planck formalism is accurate even for large impurity content.

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