Gauge invariance and Weyl-polymer quantization /
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| Author / Creator: | Strocchi, F., author. |
|---|---|
| Imprint: | Cham : Springer, ©2016. |
| Description: | 1 online resource (x, 97 pages) |
| Language: | English |
| Series: | Lecture Notes in Physics, 0075-8450 ; volume 904 Lecture notes in physics ; v. 904. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11251076 |
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| 100 | 1 | |a Strocchi, F., |e author. |0 http://id.loc.gov/authorities/names/n85306331 | |
| 245 | 1 | 0 | |a Gauge invariance and Weyl-polymer quantization / |c Franco Strocchi. |
| 264 | 1 | |a Cham : |b Springer, |c ©2016. | |
| 300 | |a 1 online resource (x, 97 pages) | ||
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| 490 | 1 | |a Lecture Notes in Physics, |x 0075-8450 ; |v volume 904 | |
| 505 | 0 | |a 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. | |
| 504 | |a Includes bibliographical references and index. | ||
| 546 | |a English. | ||
| 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 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. | ||
| 650 | 0 | |a Gauge invariance. |0 http://id.loc.gov/authorities/subjects/sh85053535 | |
| 650 | 0 | |a Physics. |0 http://id.loc.gov/authorities/subjects/sh85101653 | |
| 650 | 0 | |a Mathematical physics. |0 http://id.loc.gov/authorities/subjects/sh85082129 | |
| 650 | 0 | |a Quantum field theory. |0 http://id.loc.gov/authorities/subjects/sh85109461 | |
| 650 | 0 | |a String models. |0 http://id.loc.gov/authorities/subjects/sh85129017 | |
| 650 | 0 | |a Quantum theory. |0 http://id.loc.gov/authorities/subjects/sh85109469 | |
| 650 | 0 | |a Particles (Nuclear physics) |0 http://id.loc.gov/authorities/subjects/sh85098374 | |
| 650 | 2 | 4 | |a Elementary Particles, Quantum Field Theory. |
| 650 | 2 | 4 | |a Mathematical Physics. |
| 650 | 2 | 4 | |a Quantum Field Theories, String Theory. |
| 650 | 2 | 4 | |a Quantum Physics. |
| 650 | 4 | |a Atomic Physics. | |
| 650 | 4 | |a Physics. | |
| 650 | 4 | |a Physical Sciences & Mathematics. | |
| 650 | 7 | |a Gauge invariance. |2 fast |0 (OCoLC)fst00938998 | |
| 650 | 7 | |a Mathematical physics. |2 fast |0 (OCoLC)fst01012104 | |
| 650 | 7 | |a Particles (Nuclear physics) |2 fast |0 (OCoLC)fst01054130 | |
| 650 | 7 | |a Physics. |2 fast |0 (OCoLC)fst01063025 | |
| 650 | 7 | |a Quantum field theory. |2 fast |0 (OCoLC)fst01085105 | |
| 650 | 7 | |a Quantum theory. |2 fast |0 (OCoLC)fst01085128 | |
| 650 | 7 | |a String models. |2 fast |0 (OCoLC)fst01135293 | |
| 655 | 4 | |a Electronic books. | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319176949 |
| 830 | 0 | |a Lecture notes in physics ; |v v. 904. |x 0075-8450 |0 http://id.loc.gov/authorities/names/n42015167 | |
| 880 | |6 520-00/(S |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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| 928 | |t Library of Congress classification |a QC174.45 |l Online |c UC-FullText |u https://link.springer.com/10.1007/978-3-319-17695-6 |z Springer Nature |g ebooks |i 12533869 | ||