Five Lectures on SupersymmetryAmerican Mathematical Soc. - 119 страница Since physicists introduced supersymmetry in the mid 1970s, there have been great advances in the understanding of supersymmetric quantum field theories and string theories. These advances have had important mathematical consequences as well. The lectures featured in this book treat fundamemtal concepts necessary for understanding the physics behind these mathematical applications. Freed approaches the topic with the assumption that the basic notions of supersymmetric field theory are unfamiliar to most mathematicians. He presents the material intending to impart a firm grounding in the elementary ideas. The first half of the book offers expository introductions to superalgebras, supermanifolds, classical field theory, free quantum theories, and super Poincaré groups. The second half covers specific models and describes some of their geometric features. The overall aim is to explain the classical supersymmetric field theories that are basic for applications in quantum mechanics and quantum field theory, thereby providing readers with sufficient background to explore the quantum ideas. |
Садржај
| 5 | |
Lagrangians and Symmetries | 25 |
Supersymmetry in Various Dimensions | 47 |
LECTURE 4 Theories with Two Supersymmetries | 69 |
Theories with More Supersymmetry | 87 |
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Чести термини и фразе
abelian affine space auxiliary field bosonic central extension chiral superfield classical field theory classical solutions Clifford complex component fields component lagrangian compute connection consider constrained coordinates curvature define derivatives differential dimensional reduction dimensions discussion effective lagrangian energy equation of motion example fermions gauge field gauge group gauge theory geometry global grad h hamiltonian Hilbert space hyperkähler infinitesimal symmetry integral irreducible Kähler lagrangian field theory Lecture Lie algebra lightcone linear little group massive massless scalar metric minimal Minkowski spacetime moduli space moment map nilpotent Noether charge Noether current nonmanifest nontrivial nonzero o-model odd elements odd vector Poincaré group Poisson bracket potential quantization quantum field theory real spin representation scalar fields space of classical space of fields spinor fields super Poincaré group superalgebra supermanifold superparticle superspacetime formulation supersymmetric theory supersymmetry algebra supersymmetry group Sym² symplectic form transformations vector field vector multiplet vector space
Популарни одломци
Страница 113 - Supersymmetry and supergravity," Princeton Series in Physics, Princeton University Press, Princeton, NJ, 1983. [Wt] PC West (ed.), "Supersymmetry: a decade of development," Adam Hilger, Bristol, GB, 1986.
Страница 6 - The state of a quantum mechanical system is represented by a vector (or line) in a complex Hilbert space.