Gauge Invariance and Weyl-polymer Quantization

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Quantum Theory
Cover of the book Gauge Invariance and Weyl-polymer Quantization by Franco Strocchi, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Franco Strocchi ISBN: 9783319176956
Publisher: Springer International Publishing Publication: November 12, 2015
Imprint: Springer Language: English
Author: Franco Strocchi
ISBN: 9783319176956
Publisher: Springer International Publishing
Publication: November 12, 2015
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book An Introduction to Harmony Search Optimization Method by Franco Strocchi
Cover of the book Plato by Franco Strocchi
Cover of the book Intelligent Computing Theories and Application by Franco Strocchi
Cover of the book Artificial Intelligence in Medicine by Franco Strocchi
Cover of the book Medicine as a Scholarly Field: An Introduction by Franco Strocchi
Cover of the book Design of an Intelligent Embedded System for Condition Monitoring of an Industrial Robot by Franco Strocchi
Cover of the book The BBC and the Development of Anglophone Caribbean Literature, 1943-1958 by Franco Strocchi
Cover of the book Multidetector-Row CT of the Thorax by Franco Strocchi
Cover of the book Radiation Physics for Medical Physicists by Franco Strocchi
Cover of the book Nanofabrication by Franco Strocchi
Cover of the book The Past, Present, and Future of the Business School by Franco Strocchi
Cover of the book Towards an EU-Taiwan Investment Agreement by Franco Strocchi
Cover of the book Trends in Artificial Intelligence: PRICAI 2016 Workshops by Franco Strocchi
Cover of the book The Economics of the Global Environment by Franco Strocchi
Cover of the book Synergy Value and Strategic Management by Franco Strocchi
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy