LEADER 04480nam 22007335 450 001 9911021961203321 005 20250826130144.0 010 $a3-031-95823-3 024 7 $a10.1007/978-3-031-95823-6 035 $a(MiAaPQ)EBC32273020 035 $a(Au-PeEL)EBL32273020 035 $a(CKB)40426792400041 035 $a(DE-He213)978-3-031-95823-6 035 $a(EXLCZ)9940426792400041 100 $a20250826d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aQuantum Spin and Representations of the Poincaré Group, Part II $eWith a Focus on Physics and Operator Theory /$fby Horst R. Beyer 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (218 pages) 225 1 $aSynthesis Lectures on Engineering, Science, and Technology,$x2690-0327 311 08$a3-031-95822-5 327 $aIntroduction -- Construction of a Double Cover of the Restricted Lorentz Group -- Weyl Spinors -- Weyl Representation of SL(2, C) -- An Extension to a Strongly Continuous Representation of a Semi-direct Product of R^4 and SL(2, C) -- Dirac Spinors -- Dirac Fields -- Dirac Equation -- Spin 1 Representations of SL(2, C) -- Maxwell Fields -- Maxwell's Equations -- Appendix -- Bibliography -- Index of Symbols -- Index. 330 $aThis book discusses how relativistic quantum field theories must transform under strongly continuous unitary representations of the Poincaré group. The focus is on the construction of the representations that provide the basis for the formulation of current relativistic quantum field theories of scalar fields, the Dirac field, and the electromagnetic field. Such construction is tied to the use of the methods of operator theory that also provide the basis for the formulation of quantum mechanics, up to the interpretation of the measurement process. In addition, since representation spaces of primary interest in quantum theory are infinite dimensional, the use of these methods is essential. Consequently, the book also calculates the generators of relevant strongly continuous one-parameter groups that are associated with the representations and, where appropriate, the corresponding spectrum. Part II of Quantum Spin and Representations of the Poincaré Group specifically addresses: construction of a double cover of the restricted Lorentz Group; Weyl spinors; Weyl representation of SL(2, C); an extension to a strongly continuous representation of a semi-direct product of R^4 and SL(2, C); Dirac spinors; Dirac fields; Dirac equation; Spin 1 representations of SL(2, C); Maxwell fields; and Maxwell's equations. In addition, this book: Presents how the use of methods from operator theory have become an indispensable tool for quantum field theory Connects mathematical results with their applications in physics, particularly in quantum field theory Provides mathematical rigor, introduces physical constants, and presents the dimensions of physical quantities. 410 0$aSynthesis Lectures on Engineering, Science, and Technology,$x2690-0327 606 $aParticles (Nuclear physics) 606 $aQuantum field theory 606 $aMathematical physics 606 $aQuantum theory 606 $aOperator theory 606 $aPhysics 606 $aAstronomy 606 $aElementary Particles, Quantum Field Theory 606 $aTheoretical, Mathematical and Computational Physics 606 $aQuantum Physics 606 $aOperator Theory 606 $aMathematical Physics 606 $aPhysics and Astronomy 615 0$aParticles (Nuclear physics) 615 0$aQuantum field theory. 615 0$aMathematical physics. 615 0$aQuantum theory. 615 0$aOperator theory. 615 0$aPhysics. 615 0$aAstronomy. 615 14$aElementary Particles, Quantum Field Theory. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aQuantum Physics. 615 24$aOperator Theory. 615 24$aMathematical Physics. 615 24$aPhysics and Astronomy. 676 $a530.14 700 $aBeyer$b Horst R$0725762 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911021961203321 996 $aQuantum Spin and Representations of the Poincaré Group, Part II$94429493 997 $aUNINA LEADER 01008nam0-2200289---450 001 9911043729603321 005 20251202100459.0 100 $a20251201d1876----km-y0itay50------ba 101 1 $aita$ceng 102 $aIT 105 $ay-------001yy 200 1 $aTrattato sulle zone petroleifere d'Italia$fdi E. John Fairman$gtraduzione dall'inglese Achille Donzelli 210 $aBologna$cStab. Tip. Monti$d1876 215 $a116 p.$d22 cm 300 $aTrad. italiana dell'ed.: Londra : E.F.N. Spon, 1868. 610 0 $aPetrolio$aItalia 676 $a343$v23$zita 700 1$aFairman St. John,$bEdward$01739571 702 1$aDonzelli,$bAchille 801 0$aIT$bUNINA$gREICAT$2UNIMARC 856 4 $zVisualizza la versione elettronica in EROMM$uhttps://babel.hathitrust.org/cgi/pt?id=uiug.30112068976965&seq=9$e20251201 901 $aBK 912 $a9911043729603321 952 $aM 3 II 31$b26569$fNAP14 959 $aNAP14 996 $aTrattato sulle zone petroleifere d'Italia$94460044 997 $aUNINA