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Gauge invariance and Weyl-polymer qu...

Strocchi, Franco.

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Gauge invariance and Weyl-polymer quantization

Record Type:	Electronic resources : Monograph/item
Title/Author:	Gauge invariance and Weyl-polymer quantization/ by Franco Strocchi.
Author:	Strocchi, Franco.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	x, 97 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Heisenberg quantization and Weyl quantization -- Delocalization, gauge invariance and non-regular representations -- Quantum mechanical gauge models -- Non-regular representations in quantum field theory -- Diffeomorphism invariance and Weyl polymer quantization -- A generalization of Stone-von Neumann theorem -- Bibliography -- Index.
Contained By:	Springer eBooks
Subject:	Gauge invariance. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-17695-6
ISBN:	9783319176956$q(electronic bk.)

Gauge invariance and Weyl-polymer quantization
Strocchi, Franco.

Gauge invariance and Weyl-polymer quantization[electronic resource] /by Franco Strocchi. - Cham :Springer International Publishing :2016. - x, 97 p. :ill., digital ;24 cm. - Lecture notes in physics,v.9040075-8450 ;. - Lecture notes in physics ;715..

Introduction -- Heisenberg quantization and Weyl quantization -- Delocalization, gauge invariance and non-regular representations -- Quantum mechanical gauge models -- Non-regular representations in quantum field theory -- Diffeomorphism invariance and Weyl polymer quantization -- A generalization of Stone-von Neumann theorem -- Bibliography -- Index.

The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the traditional Dirac-Heisenberg quantization is not applicable. The latter implicitly assumes that the canonical variables describe observables, entailing necessarily the regularity of their exponentials (Weyl operators) However, in physically interesting cases -- typically in the presence of a gauge symmetry -- non-observable canonical variables are introduced for the description of the states, namely of the relevant representations of the observable algebra. In general, a gauge invariant ground state defines a non-regular representation of the gauge dependent Weyl operators, providing a mathematically consistent treatment of familiar quantum systems -- such as the electron in a periodic potential (Bloch electron), the Quantum Hall electron, or the quantum particle on a circle -- where the gauge transformations are, respectively, the lattice translations, the magnetic translations and the rotations of 2π. Relevant examples are also provided by quantum gauge field theory models, in particular by the temporal gauge of Quantum Electrodynamics, avoiding the conflict between the Gauss law constraint and the Dirac-Heisenberg canonical quantization. The same applies to Quantum Chromodynamics, where the non-regular quantization of the temporal gauge provides a simple solution of the U(1) problem and a simple link between the vacuum structure and the topology of the gauge group. Last but not least, Weyl non-regular quantization is briefly discussed from the perspective of the so-called polymer representations proposed for Loop Quantum Gravity in connection with diffeomorphism invariant vacuum states.

ISBN: 9783319176956$q(electronic bk.)

Standard No.: 10.1007/978-3-319-17695-6doiSubjects--Topical Terms:

716126
Gauge invariance.

LC Class. No.: QC174.45

Dewey Class. No.: 530.12

Gauge invariance and Weyl-polymer quantization
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520 $a The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the traditional Dirac-Heisenberg quantization is not applicable. The latter implicitly assumes that the canonical variables describe observables, entailing necessarily the regularity of their exponentials (Weyl operators) However, in physically interesting cases -- typically in the presence of a gauge symmetry -- non-observable canonical variables are introduced for the description of the states, namely of the relevant representations of the observable algebra. In general, a gauge invariant ground state defines a non-regular representation of the gauge dependent Weyl operators, providing a mathematically consistent treatment of familiar quantum systems -- such as the electron in a periodic potential (Bloch electron), the Quantum Hall electron, or the quantum particle on a circle -- where the gauge transformations are, respectively, the lattice translations, the magnetic translations and the rotations of 2π. Relevant examples are also provided by quantum gauge field theory models, in particular by the temporal gauge of Quantum Electrodynamics, avoiding the conflict between the Gauss law constraint and the Dirac-Heisenberg canonical quantization. The same applies to Quantum Chromodynamics, where the non-regular quantization of the temporal gauge provides a simple solution of the U(1) problem and a simple link between the vacuum structure and the topology of the gauge group. Last but not least, Weyl non-regular quantization is briefly discussed from the perspective of the so-called polymer representations proposed for Loop Quantum Gravity in connection with diffeomorphism invariant vacuum states.
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