Reflections on Quanta, Symmetries, and Supersymmetries

ISBN-13: 9781441906663 / Angielski / Twarda / 2011 / 236 str.

V. S. Varadarajan

Opis

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 unkown 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.

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.

Recenzje

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)

Spis treści

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.

O autorze

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."

Blurb

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.