Y. Ohnuki, S. Kamefuchi

Quantum Field Theory and Parastatistics

• Broschiertes Buch

Produktbeschreibung

In examining the problem of quantization it is customary to proceed by following the order of historical developments, i. e. , to start with the so-called first quantization and then go on to second, or field, quantization. As is well known, the former consists in setting up commutation relations among the canonical variables (of finite degrees of freedom) which are defined originally in classical mechanics, and the latter consists in doing the same among field variables. In our opinion, however, the above order does not necessarily reflect that of physical importance. In fact, a close look at the theoretical that the latter plays a more fundamental role structure immediately reveals than the former in various respects. First, the former can be derived from the latter, and second, the assumptions that have to be made in the former, e. g. the spin-statistics connection, can be justified in the latter on the basis of its own theory. Furthermore, as the history of the positron theory shows, if we remain within the framework of the first-quantized formalism, it will no longer be possible to have a closed theory in the relativistic region where the problem becomes essentially that of an infinite number of particles.

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Produktdetails

• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-642-68624-5
• Softcover reprint of the original 1st ed. 1982
• Seitenzahl: 508
• Erscheinungstermin: 7. Dezember 2011
• Englisch
• Abmessung: 229mm x 152mm x 28mm
• Gewicht: 727g
• ISBN-13: 9783642686245
• ISBN-10: 3642686249
• Artikelnr.: 36115141

Inhaltsangabe

I. Paraquantization.- 1. Canonical Quantization and Its Generalization.- 2. The Case of a Simple Harmonic Oscillator.- 3. The Case of More than One Oscillator.- 4. The Order of Paraquantization.- 5. Realization of the Paracommutation Relations.- 6. General Algebraic Relations.- II. Non-Relativistic Field Theory the case of a single parafield.- 7. Quantization of a de Broglie Field.- 8. Properties of State Vectors.- 9. The Structure of Observables.- 10. Gauge Groups.- 11. The Relation to an Ordinary Field with a Hidden Variable.- III. Non-Relativistic Field Theory the case of coexisting parafields.- 12. Commutation Relations between Different Parafields.- 13. Generalization of the Decomposition- and Related Theorems.- 14. Families and Gauge Groups.- 15. The Overall Structure of Observables.- 16. Bound States.- 17. Superselection Rules.- IV. Relativistic Field Theory.- 18. Relativization.- 19. Relativistic Parafermi Fields of Order 2.- 20. Discrete Transformations in Space-Time.- 21. The Variational Principle.- 22. Application to Particle Physics.- V. Miscellaneous Problems.- 23. The Wave-Mechanical Representation for a Bose-Like Oscillator.- 24. The Method of h-polynomials.- 25. First-Quantized Formalism of Identical Particles.- 26. Fermi-Bose Similarity.- 27. Paragrassmann Algebras and Parafermi Systems.- Appendices.- Appendix B. A Self-Contained Set of Commutation Relations for p =3.- Appendix D. Proof of (8.64).- Appendix E. The Decomposition U(p) ? O(p).- Appendix F. The Normal and Anomalous Cases of Commutation Relations in Ordinary Field Theory.- Appendix G. A Formal Generalization of Lie Algebras and Lie Groups.- Appendix H. Generalized Grassmann Numbers.- Appendix I. Generalized Bose Numbers.- References.- Further References.- List of Special Symbols.