Essays on Supersymmetry

ISBN-13: 9789401085557 / Angielski / Miękka / 2011 / 280 str.

C. Fronsdal; M. Flato; T. Hirai

Opis

to our own also needs to be understood. Such unification may also require that the supersymmetry group possess irreducible representations with infinite reductiori on the Poincare subgroup, to accommodate an infinite set of particles. Such possibilities were 5 envisaged long ago and have recently reappeared in Kaluza-Klein . 6 d' . th 7 S . l' th supergraVlty an m superstnng eory. upersymmetry Imp Ies at forces that are mediated by bose exchange must be complemented by forces that are due to the exchange of fermions. The masslessness of neutrinos is suggestive-we continue to favor the idea that neutrinos are fundamental to weak interactions, that they will finally play a more central role than the bit part assigned to them in Weinberg-Salam theory. There seems to be little room for doubting that supersymmetry is badly broken-so where should one be looking for the first tangible manifestations of it? It is remarkable that the successes that can be legitimately claimed for supersymmetry are all in the domain of massless particles and fields. Supergravity is not renormalizable, but it is an improvement (in this respect) over ordinary quantum gravity. Finite super Yang-Mills theories are not yet established, but there is now a strong concensus that they soon will be. In both cases massless fields are involved in an essential way.

Spis treści

1. Why supersymmetry?.- 2. Why in de Sitter space?.- 3. Why group theory?.- 4. Background.- 5. This book, summary.- 6. Future directions.- Unitary Representations of Supergroups.- 0. Introduction..- 1. General structural problems.- 2. Invariant Hermitean forms.- 3. An example: osp(2n/l).- 3+2 De Sitter Superfields.- 0. Introduction.- 1. Superfields and induced representations.- 2. Induction from an irreducible representation.- 3. Invariant operators.- 4. Massive superfields, “scalar” multiplet.- 5. The “vector” multiplet.- 6. The simplest superfield for N = 2 supersymmetry.- 7. Induction from an irreducible representation.- 8. Wave equations for N = 2.- 9. The spinor superfield and de Sitter chirality.- Appendices.- Al. Linear action for osp(2n/l).- A2. Linear action for osp(2n/2).- A3. Intertwining operators.- A4. Invariant fields.- Spontaneously Generated Field Theories, Zero-Center Modules, Colored Singletons and the Virtues of N = 6 Supergravity.- 0. Introduction.- 1. De Sitter electrodynamics.- 2. Conformal electrodynamics.- 3. De Sitter super electrodynamics.- 4. Extended de Sitter super electrodynamics.- 5. Super conformal electrodynamics.- 6. Extended super conformal electrodynamics.- Massless Particles, Orthosymplectic Symmetry and Another Type of Kaluza-Klein Theory.- 0. Introduction.- I. Geometric preliminaries.- 1. Phase space, sp(2n,R) and osp(2n/l).- 2. The oscillator representation.- II. Superfield preliminaries.- 3. Superfield representation.- 4. Oscillator representation on superfields.- III. Algebraic representation theory.- 5. Lowest weight representations of sp(2n).- 6. K-structure.- 7. Non-decomposable representations of sp(2n).- 8. Lowest weight representations of osp(2n/l).- IV. Homogeneous space and line bundle.- 9. The homogeneous space X.- 10. Parameterization of X.- 11. The line bundle Z? over X.- 12. The oscillator representation on Z?1/2.- V. Physical interpretation.- 13. The conformal group U?(n).- 14. Identification of space time.- 15. The other orbits of U? (n).- 16. Interpretation of the extra dimensions.- 17. Irreducible u? (n) modules.- VI. Scalar field on space time.- 18. Scalar field on Dirac’s projective cone.- 19. Quasi-invariant wave operator on U(2).- 20. The conformal tube.- 21. Hilbert space of holomorphic functions.- 22. Invariant bilinear functionals.- 23. Cauchy kernel and Lagrangian.- VII. osp(8) field theory--a beginning.- 24. Intertwining operators.- 25. Lagrangian and wave equation.- 26. The reduced superfield.