LEADER 03773nam 22005655 450 001 9910485026803321 005 20200703003213.0 010 $a981-15-2180-8 024 7 $a10.1007/978-981-15-2180-5 035 $a(CKB)4100000010159514 035 $a(DE-He213)978-981-15-2180-5 035 $a(MiAaPQ)EBC6037187 035 $a(PPN)242977219 035 $a(EXLCZ)994100000010159514 100 $a20200204d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInequivalent Representations of Canonical Commutation and Anti-Commutation Relations $eRepresentation-theoretical Viewpoint for Quantum Phenomena /$fby Asao Arai 205 $a1st ed. 2020. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2020. 215 $a1 online resource (XIX, 493 p. 6 illus.) 225 1 $aMathematical Physics Studies,$x0921-3767 311 $a981-15-2179-4 327 $aMathematical Preliminaries -- Representations of Canonical Commutation Relations with Finite -- Aharonov?Bohm Effect and Inequivalent Representations of CCR -- Time Operators -- Representations of Canonical Anti-commutation Relations with Finite Degrees of Freedom -- Elements of the Theory of Boson Fock Spaces -- Elements of the Theory of Fermion Fock Spaces -- Representations of CCR with Infinite Degrees of Freedom -- Representations of CAR with Infinite Degrees of Freedom -- Physical Correspondences in Quantum Field Theory. 330 $aCanonical commutation relations (CCR) and canonical anti-commutation relations (CAR) are basic principles in quantum physics including both quantum mechanics with finite degrees of freedom and quantum field theory. From a structural viewpoint, quantum physics can be primarily understood as Hilbert space representations of CCR or CAR. There are many interesting physical phenomena which can be more clearly understood from a representation?theoretical viewpoint with CCR or CAR. This book provides an introduction to representation theories of CCR and CAR in view of quantum physics. Particular emphases are put on the importance of inequivalent representations of CCR or CAR, which may be related to characteristic physical phenomena. The topics presented include general theories of representations of CCR and CAR with finite and infinite degrees of freedom, the Aharonov?Bohm effect, time operators, quantum field theories based on Fock spaces, Bogoliubov transformations, and relations of infinite renormalizations with inequivalent representations of CCR. This book can be used as a text for an advanced topics course in mathematical physics or mathematics. 410 0$aMathematical Physics Studies,$x0921-3767 606 $aMathematical physics 606 $aQuantum physics 606 $aFunctional analysis 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aMathematical physics. 615 0$aQuantum physics. 615 0$aFunctional analysis. 615 14$aMathematical Physics. 615 24$aQuantum Physics. 615 24$aFunctional Analysis. 676 $a530.12 700 $aArai$b Asao$4aut$4http://id.loc.gov/vocabulary/relators/aut$0976151 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910485026803321 996 $aInequivalent Representations of Canonical Commutation and Anti-Commutation Relations$92223248 997 $aUNINA