LEADER 05981nam 2200757 a 450 001 9910786472503321 005 20200520144314.0 010 $a1-283-62764-7 010 $a3-11-916337-6 010 $a9786613940094 024 7 $a10.1515/9783110250633 035 $a(CKB)2670000000279371 035 $a(EBL)894113 035 $a(OCoLC)993343088$z(OCoLC)811964412 035 $a(SSID)ssj0001036332 035 $a(PQKBManifestationID)11577003 035 $a(PQKBTitleCode)TC0001036332 035 $a(PQKBWorkID)11041924 035 $a(PQKB)11499916 035 $a(MiAaPQ)EBC894113 035 $a(DE-B1597)122986 035 $a(OCoLC)1013950393 035 $a(OCoLC)801874117 035 $a(DE-B1597)9783110250633 035 $a(Au-PeEL)EBL894113 035 $a(CaPaEBR)ebr10606462 035 $a(CaONFJC)MIL394009 035 $a(OCoLC)811964412 035 $a(PPN)182937208 035 $a(EXLCZ)992670000000279371 100 $a20120405d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTheory of interacting quantum fields$b[electronic resource] /$fAlexei L. Rebenko 210 $aBerlin ;$aBoston $cDe Gruyter$dc2012 215 $a1 online resource (588 p.) 225 0 $aDe Gruyter Studies in Mathematics ;$v39 225 0$aDe Gruyter studies in mathematics,$x0179-0986 ;$v39 300 $aDescription based upon print version of record. 311 $a3-11-025063-2 311 $a3-11-025062-4 320 $aIncludes bibliographical references (p. [549]-561) and index. 327 $t Frontmatter -- $tPreface -- $tNotation -- $tContents -- $tChapter 0. Introduction -- $tPart I. Symmetry Groups of Elementary Particles -- $tChapter 1. Lorentz Group -- $tChapter 2. Groups of Internal Symmetries -- $tChapter 3. Problems to Part I -- $tPart II. Classical Theory of the Free Fields -- $tChapter 4. Lagrangian and Hamiltonian Formalisms of the Classical Field Theory -- $tChapter 5. Classical Theory of Free Scalar Fields -- $tChapter 6. Spinor Field -- $tChapter 7. Vector Fields -- $tChapter 8. Electromagnetic Field -- $tChapter 9. Equations for Fields with Higher Spins -- $tChapter 10. Problems to Part II -- $tPart III. Classical Theory of Interacting Fields -- $tChapter 11. Gauge Theory of the Electromagnetic Interaction -- $tChapter 12. Classical Theory of Yang-Mills Fields -- $tChapter 13. Masses of Particles and Spontaneous Breaking of Symmetry -- $tChapter 14. On the Construction of the General Lagrangian of Interacting Fields -- $tChapter 15. Solutions of the Equations for Classical Fields: Solitary Waves, Solitons, Instantons -- $tChapter 16. Problems to Part III -- $tPart IV. Second Quantization of Fields -- $tChapter 17. Axioms and General Principles of Quantization -- $tChapter 18. Quantization of the Free Scalar Field -- $tChapter 19. Quantization of the Free Spinor Field -- $tChapter 20. Quantization of the Vector and Electromagnetic Fields. Specific Features of the Quantization of Gauge Fields -- $tChapter 21. CPT. Spin and Statistics -- $tChapter 22. Representations of Commutation and Anticommutation Relations -- $tChapter 23. Green Functions -- $tChapter 24. Problems to Part IV -- $tPart V. Quantum Theory of Interacting Fields. General Problems -- $tChapter 25. Construction of Quantum Interacting Fields and Problems of This Construction -- $tChapter 26. Scattering Theory. Scattering Matrix -- $tChapter 27. Equations for Coefficient Functions of the S-Matrix -- $tChapter 28. Green Functions and Scattering Matrix -- $tChapter 29. On Renormalization in Perturbation Theory -- $tChapter 30. Method of Functional (Path) Integrals in Quantized Field Theory -- $tChapter 31. Problems to Part V -- $tPart VI. Axiomatic and Euclidean Field Theories -- $tChapter 32. Wightman Axiomatics -- $tChapter 33. Other Axiomatic Approaches -- $tChapter 35. Euclidean Axiomatics -- $tChapter 36. Problems to Part VI -- $tPart VII. Quantum Theory of Gauge Fields -- $tChapter 37. Quantum Electrodynamics (QED) -- $tChapter 38. Quantization of Gauge Fields -- $tChapter 39. Standard Models of Interactions -- $tChapter 40. Problems to Part VII -- $tAppendix. Hints for the Solution of Problems -- $tBibliography -- $tIndex 330 $aThis monograph is devoted to the systematic presentation of foundations of the quantum field theory. Unlike numerous monographs devoted to this topic, a wide range of problems covered in this book are accompanied by their sufficiently clear interpretations and applications. An important significant feature of this monograph is the desire of the author to present mathematical problems of the quantum field theory with regard to new methods of the constructive and Euclidean field theory that appeared in the last thirty years of the 20th century and are based on the rigorous mathematical apparatus of functional analysis, the theory of operators, and the theory of generalized functions. The monograph is useful for students, post-graduate students, and young scientists who desire to understand not only the formality of construction of the quantum field theory but also its essence and connection with the classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of path integral formalism. 410 3$aDe Gruyter Studies in Mathematics 606 $aQuantum field theory 610 $aBernstein Function. 610 $aMonotonic Function. 610 $aOperator Theory. 610 $aProbability Measure. 610 $aSemigroup. 615 0$aQuantum field theory. 676 $a530.14/3 686 $aUO 4000$2rvk 700 $aRebenko$b Aleksei? Lukich$01536593 701 $aMalyshev$b Peter V$01536594 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910786472503321 996 $aTheory of interacting quantum fields$93785449 997 $aUNINA