Reflections on Quanta, Symmetries, and Supersymmetries - Varadarajan, V.S.; SpringerLink (Online service) (New York, NY : Springer New York, 2011)
Unitary representation theory has great intrinsic beauty which enters other parts of mathematics at a very deep level. In quantum physics it is the preferred language for describing symmetries and supersymmetries. Two of the greatest figures in its history are Mackey and Harish-Chandra. Their work (to use the words of Weyl) affords shade to large parts of present day mathematics and high energy physics. It is to their memory that this volume is lovingly dedicated. Mackey and Harish-Chandra. Their work (to use the words of Weyl) affords shade to large parts of present day mathematics and high energy physics. It is to their memory that this volume is lovingly dedicated. The essays in this volume are like a stroll through a garden of ideas of this rich subject: quantum algebras, super geometry, unitary supersymmetries, differential equations, non-archimedean physics, are a few of the topics encountered along the way. The author, whose mathematical education evolved out of his interactions with Mackey and Harish-Chandra, concludes this volume with brief portraits of their work, embedded in the context of personal reminiscences.
Prologue -- Quantum foundations -- Quantum measurement -- Probability in the quantum world -- Spacetime in the ultra-small scale -- The superworld -- Symmetries and particles in the p-adic world -- Representation theory: Conversations with Harish-Chandra.
Keywords: Mathematics; Algebra; Topological Groups; Differential Equations; Distribution (Probability theory).; Quantum theory; Mathematics; Topological Groups, Lie Groups; Quantum Physics; Order, Lattices, Ordered Algebraic Structures; Elementary Particles, Quantum Field Theory; Ordinary Differential Equations; Probability Theory and Stochastic Processes