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Reflections on Quanta, Symmetries, and Supersymmetries

  • Book
  • © 2011

Overview

Authors:
  1. V.S. Varadarajan

    1. Department of Mathematics, UCLA, Los Angeles, USA

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  • The author's interest in representation is lifelong

  • Explores the Volovich hypothesis that the world of ultra-small times and distances is non-archimedean

  • Concludes with a retrospective look at the author's discussions with George Mackey and Harish-Chandra

  • Includes supplementary material: sn.pub/extras

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Table of contents (8 chapters)

  1. Front Matter

    Pages 1-8
    Download chapter PDF

  2. Prologue

    • V. S. Varadarajan
    Pages 1-14

  3. Quantum Algebra

    • V. S. Varadarajan
    Pages 15-56

  4. Probability in the quantum world

    • V. S. Varadarajan
    Pages 57-91

  5. Super geometry

    • V. S. Varadarajan
    Pages 93-120

  6. Unitary representations of super Lie groups

    • V. S. Varadarajan
    Pages 121-153

  7. Nonarchimedean physics

    • V. S. Varadarajan
    Pages 155-178

  8. Differential equations with irregular singularities

    • V. S. Varadarajan
    Pages 179-205

  9. Mackey, Harish-Chandra, and representation theory

    • V. S. Varadarajan
    Pages 207-236
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Keywords

About this book

This is a collection of essays based on lectures that author has given on various occasions on foundation of quantum theory, symmetries and representation theory, and the quantum theory of the superworld created by physicists. The lectures are linked by a unifying theme: how the quantum world and superworld appear under the lens of symmetry and supersymmetry. In the world of ultra-small times and distances such as the Planck length and Planck time, physicists believe no measurements are possible and so the structure of spacetime itself is an unknown that has to be first understood. There have been suggestions (Volovich hypothesis) that world geometry at such energy regimes is non-archimedian and some of the lectures explore the consequences of such a hypothesis. Ultimately, symmetries and supersymmetries are described by the representation of groups and supergroups. The author's interest in representation is a lifelong one and evolved slowly, and owes a great deal to conversations and discussions he had with George Mackey and Harish-Chandra. The book concludes with a retrospective look at these conversations.

Reviews

From the reviews:

“This volume is a marvelous collection of essays that marries the technical with the personal. The technical part is an exploration of symmetries that arise in considerations of quantum theory. The personal part consists of reminiscences by the author about his colleagues … . Each essay provides a list of readings for those who wish to pursue the subject in greater depth.” (William G. Faris, SIAM Review, Vol. 54 (1), 2012)

“Present book is an inspiring collection of essays and lectures the author has given at various places. … The book has eight chapters containing many personal reflections. … The book provides an impressively lucid presentation of the mentioned topics and will prove invaluable both to students as well as research workers in physics and mathematics.” (Gert Roepstorff, Zentralblatt MATH, Vol. 1222, 2011)

“Varadarajan’s Reflections on Quanta, Symmetries, and Supersymmetries is a wonderful collection of essays by a master of the genre … presented in a compact fashion richly peppered with pithy personal remarks, both biographical and autobiographical. I dearly love Professor Varadarajan, and I am ecstatic at having a copy of this book all my own. Get a copy, too.” (Michael Berg, The Mathematical Association of America, July, 2011)

Authors and Affiliations

  • Department of Mathematics, UCLA, Los Angeles, USA

    V.S. Varadarajan

About the author

The author writes: "Most of my thoughts on quantum theory are in these essays. The last section is on represenation theory. I do not like to call it an epilogue bucause it deals with a large part of what I have done in this area over the years...I have been thinking about a collection like this for many years that will bring together the many lectures I have given in various places."

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