LEADER 04387nam 22007095 450 001 9910254637003321 005 20251202115532.0 010 $a3-319-25901-6 024 7 $a10.1007/978-3-319-25901-7 035 $a(CKB)3710000000616260 035 $a(EBL)4453015 035 $a(SSID)ssj0001653754 035 $a(PQKBManifestationID)16433685 035 $a(PQKBTitleCode)TC0001653754 035 $a(PQKBWorkID)14982100 035 $a(PQKB)10755703 035 $a(DE-He213)978-3-319-25901-7 035 $a(MiAaPQ)EBC4453015 035 $a(PPN)192772155 035 $a(EXLCZ)993710000000616260 100 $a20160316d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPerturbative Algebraic Quantum Field Theory $eAn Introduction for Mathematicians /$fby Kasia Rejzner 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (186 p.) 225 1 $aMathematical Physics Studies,$x2352-3905 300 $aDescription based upon print version of record. 311 08$a3-319-25899-0 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Algebraic approach to quantum theory -- Algebraic quantum mechanics -- Causality -- Haag-Kastler axioms -- pAQFT axioms -- LCQFT -- Kinematical structure -- The space of field configurations -- Functionals on the configuration space -- Fermionic field configurations -- Vector fields -- Functorial interpretation -- Classical theory -- Dynamics -- Natural Lagrangians -- Homological characterization of the solution space -- The net of topological Poisson algabras -- Analogy with classical mechanics -- Deformation quantization -- Star products -- The star product on the space of multivector fields -- Kähler structure -- Interaction -- Outline of the approach -- Scatering matrix and time ordered products -- Renormalization group -- Interacting local nets -- Explicit construction -- Gauge theories -- Classical gauge theory -- Gauge-fixing -- BV formalism -- Effective quantum gravity -- From LCQFT to quantum gravity -- Dynamics and symmetries -- Linearized theory -- Quantization -- Relational observables -- Background independence. 330 $aPerturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn?t require the use of divergent quantities. We discuss in detail the examples of scalar fields and gauge theories and generalize them to QFT on curved spacetimes. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses QFT on curved spacetimes and effective quantum gravity. The book aims to beaccessible researchers and graduate students interested in the mathematical foundations of pQFT are the intended audience. 410 0$aMathematical Physics Studies,$x2352-3905 606 $aElementary particles (Physics) 606 $aQuantum field theory 606 $aMathematical physics 606 $aAlgebraic fields 606 $aPolynomials 606 $aElementary Particles, Quantum Field Theory 606 $aMathematical Physics 606 $aField Theory and Polynomials 615 0$aElementary particles (Physics). 615 0$aQuantum field theory. 615 0$aMathematical physics. 615 0$aAlgebraic fields. 615 0$aPolynomials. 615 14$aElementary Particles, Quantum Field Theory. 615 24$aMathematical Physics. 615 24$aField Theory and Polynomials. 676 $a530.143 700 $aRejzner$b Kasia$4aut$4http://id.loc.gov/vocabulary/relators/aut$0808623 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254637003321 996 $aPerturbative Algebraic Quantum Field Theory$92528323 997 $aUNINA