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001 978-3-319-17695-6
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008 151112s2016 gw | s |||| 0|eng d
020 _a9783319176956
_9978-3-319-17695-6
024 7 _a10.1007/978-3-319-17695-6
_2doi
050 4 _aQC173.96-174.52
072 7 _aPHQ
_2bicssc
072 7 _aSCI057000
_2bisacsh
072 7 _aPHQ
_2thema
082 0 4 _a530.12
_223
100 1 _aStrocchi, Franco.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aGauge Invariance and Weyl-polymer Quantization
_h[electronic resource] /
_cby Franco Strocchi.
250 _a1st ed. 2016.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aX, 97 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v904
505 0 _aIntroduction -- 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.
520 _aThe 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.
650 0 _aQuantum theory.
650 1 4 _aQuantum Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19080
650 2 4 _aMathematical Physics.
_0http://scigraph.springernature.com/things/product-market-codes/M35000
650 2 4 _aQuantum Field Theories, String Theory.
_0http://scigraph.springernature.com/things/product-market-codes/P19048
650 2 4 _aElementary Particles, Quantum Field Theory.
_0http://scigraph.springernature.com/things/product-market-codes/P23029
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319176949
776 0 8 _iPrinted edition:
_z9783319176963
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v904
856 4 0 _uhttps://doi.org/10.1007/978-3-319-17695-6
912 _aZDB-2-PHA
912 _aZDB-2-LNP
999 _c9791
_d9791