Gauge Invariance and Weyl-polymer Quantization (Paperback, 1st ed. 2016)

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 2 . 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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Lecture Notes in Physics, 904
Release date:	November 2015
First published:	2016
Authors:	Franco Strocchi
Dimensions:	235 x 155 x 10mm (L x W x T)
Format:	Paperback
Pages:	97
Edition:	1st ed. 2016
ISBN-13:	978-3-319-17694-9
Categories:	Books > Science & Mathematics > Mathematics > Applied mathematics > General Books > Science & Mathematics > Physics > Thermodynamics & statistical physics > Statistical physics Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics) > General
LSN:	3-319-17694-3
Barcode:	9783319176949

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