Five Lectures on Supersymmetry
American 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.
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a-model abelian action affine space auxiliary field bosonic central extension chiral superfield classical field theory classical solutions Clifford complex component fields component lagrangian compute connection consider constant constrained coordinates curvature define derivatives dimensional reduction dimensions discussion effective lagrangian equation of motion example fermions field f gauge field gauge group gauge theory geometry global hamiltonian Hilbert space hyperkahler infinitesimal symmetry inner product integral invariant vector fields irreducible Kahler lagrangian field theory Lecture Lie algebra lightcone linear little group Lorentz massive massless scalar metric minimal Minkowski spacetime moduli space moment map nilpotent Noether charge Noether current nonmanifest nontrivial nonzero odd elements Poincare group Poisson bracket quantization quantum field theory quantum particles quaternionic real spin representation scalar fields sign rule space of classical space of fields Spin(l spinor fields super Poincare group supermanifold superparticle superpotential superspacetime formulation supersymmetric theory supersymmetry algebra supersymmetry group symplectic form transformations vector field vector multiplet write
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