Free Delivery Over $100
|
|
|||
|
||||
OverviewFull Product DetailsAuthor: Y. Ohnuki , S. KamefuchiPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: Softcover reprint of the original 1st ed. 1982 Dimensions: Width: 15.20cm , Height: 2.50cm , Length: 22.90cm Weight: 0.728kg ISBN: 9783642686245ISBN 10: 3642686249 Pages: 490 Publication Date: 07 December 2011 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsI. Paraquantization.- 1. Canonical Quantization and Its Generalization.- 2. The Case of a Simple Harmonic Oscillator.- 2.1 A bose-like oscillator.- 2.2 A fermi-like oscillator.- 3. The Case of More than One Oscillator.- 3.1 Preliminaries of a generalization.- 3.2 Introduction of the groups SO(2f) and Sp(2f, R).- 3.3 Parafermi quantization.- 3.4 Parabose quantization.- 4. The Order of Paraquantization.- 4.1 State-vector space with the unique vacuum.- 4.2 The order p and irreducibility of the ring.- 5. Realization of the Paracommutation Relations.- 5.1 Commutation relations specific to given order p.- 5.2 The Green representation.- 6. General Algebraic Relations.- 6.1 The relation between two kinds of brackets.- 6.2 The decomposition theorem.- 6.3 Identities specific to given order p.- References.- II. Non-Relativistic Field Theory the case of a single parafield.- 7. Quantization of a de Broglie Field.- 7.1 Basic requirements for field quantization.- 7.2 Application of the paracommutation relations to field operators; parastatistics.- 8. Properties of State Vectors.- 8.1 State vectors of the standard form.- 8.2 Particle and place permutations; the symmetric group.- 8.3 Decomposition into Sn-irreducible subspaces.- 8.4 Proof of the main theorem.- 9. The Structure of Observables.- 9.1 The locality condition.- 9.2 Possible forms of observables.- 10. Gauge Groups.- 10.1 Klein transformations.- 10.2 Group-theoretical properties of state vectors.- 10.3 State vectors as representations of the gauge groups.- 10.4 Superselection operators.- 11. The Relation to an Ordinary Field with a Hidden Variable.- 11.1 Strong and weak equivalences.- 11.2 Local equivalence and cluster property.- References.- III. Non-Relativistic Field Theory the case of coexisting parafields.- 12. Commutation Relations between Different Parafields.- 12.1 Bilinear and trilinear commutation relations between two different parafields.- 12.2 Trilinear commutation relations between three different parafields.- 12.3 General properties of commutation relations.- 13. Generalization of the Decomposition- and Related Theorems.- 13.1 Preliminaries; generalized particle permutations.- 13.2 Generalization of various theorems and lemmata.- 13.3 Remarks on the transformation properties of inner products.- 14. Families and Gauge Groups.- 14.1 The spaces A and B of a family of order p.- 14.2 Observables and gauge groups.- 14.3 Exceptional cases of gauge groups.- 14.4 Redefinition of parafields and families.- 15. The Overall Structure of Observables.- 15.1 Nonlocal factors in observables.- 15.2 Introduction of an alternative set of Klein operators.- 15.3 The normal and anomalous cases of commutation relations.- 16. Bound States.- 16.1 Formulation in the space B.- 16.2 Statistics of bound states.- 16.3 Factorizability.- 17. Superselection Rules.- 17.1 Locality and conservation laws.- 17.2 Selection rules characteristic of parafields.- References.- IV. Relativistic Field Theory.- 18. Relativization.- 18.1 Relativistic fields; the spin-statistics theorem.- 18.2 Remarks on theories with the locality condition of the weak form.- 19. Relativistic Parafermi Fields of Order 2.- 19.1 Approach (I) with use of redefined observables.- 19.2 Approach (II) with use only of bilocal operators.- 20. Discrete Transformations in Space-Time.- 20.1 The CPT -transformation for ordinary fields.- 20.2 The CPT -transformation for parafields.- 20.3 The transformations P, C and T.- 21. The Variational Principle.- 21.1 The general procedure.- 21.2 Application to some simple systems.- 21.3 The structure of Lagrangians and the locality condition.- 22. Application to Particle Physics.- 22.1 Statistical types of fundamental particles.- 22.2 Leptons.- 22.3 Hadrons.- 22.4 Families of fundamental particles.- References.- V. Miscellaneous Problems.- 23. The Wave-Mechanical Representation for a Bose-Like Oscillator.- 23.1 The expression for the momentum operator.- 23.2 The eigenvalue problem of the momentum operator.- 23.3 The eigenvalue problem of the Hamiltonian.- 23.4 The relation between the two classes of eigenfunctions.- 23.5 The relations between ?n?’s and ?n’ s.- 23.6 The uncertainty relation.- 24. The Method of h-polynomials.- 24.1 The definition of h-polynomials.- 24.2 The relation between h-polynomials and dotted brackets.- 25. First-Quantized Formalism of Identical Particles.- 25.1 Identical particles without internal degrees of freedom.- 25.2 General formulas for the case of paraparticles.- 25.3 The case G = U(p).- 25.4 The cases G = O(p), SO(p).- 25.5 Remarks on further problems.- 26. Fermi-Bose Similarity.- 26.1 Lie-algebraic structure of parafield operators.- 26.2 A system of parafields transformable to one another.- 26.3 Families of parafields.- 27. Paragrassmann Algebras and Parafermi Systems.- 27.1 Paragrassmann algebras.- 27.2 Applications to parafermi systems.- References.- 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
||||
