This monograph on the description and study of representations of the rotation group of three-dimensional space and of the Lorentz group features advanced topics and techniques crucial to many areas of modern theoretical physics. Prerequisites include a familiarity with the differential and integral calculus of several variables and the fundamentals of linear algebra. Suitable for advanced undergraduate and graduate students in mathematical physics, the book is also designed for mathematicians studying the representations of Lie groups, for whom it can serve as an introduction to the general theory of representation.The treatment encompasses all the basic material of the theory of representations used in quantum mechanics. The two-part approach begins with representations of the group of rotations of three-dimensional space, analyzing the rotation group and its representations. The second part, covering representations of the Lorentz group, includes an exploration of relativistic-invariant equations. The text concludes with three helpful supplements and a bibliography.

Representations of the Rotation and Lorentz Groups and Their Applications

Science & Math

Gelfand, I.M.

Minlos R.A.

Shapiro, Z. Ya

Mathematics

Dover Publications

<p>This book presents a mathematically rigorous approach to the main ideas and phenomena of statistical physics. The introduction addresses the physical motivation, focussing on the basic concept of modern statistical physics, that is the notion of Gibbsian random fields. Properties of Gibbsian fields are analyzed in two ranges of physical parameters: ``regular'' (corresponding to high-temperature and low-density regimes) where no phase transition is exhibited, and ``singular'' (low temperature regimes) where such transitions occur. Next, a detailed approach to the analysis of the phenomena of phase transitions of the first kind, the Pirogov-Sinai theory, is presented. The author discusses this theory in a general way and illustrates it with the example of a lattice gas with three types of particles. The conclusion gives a brief review of recent developments arising from this theory. The volume is written for the beginner, yet advanced students will benefit from it as well. The book will serve nicely as a supplementary textbook for course study. The prerequisites are an elementary knowledge of mechanics, probability theory and functional analysis.</p>

Introduction to Mathematical Statistical Physics (University Lecture Series)

Amer Mathematical Society

2012 Reprint of 1963 Edition. Exact facsimile of the original edition, not reproduced with Optical Recognition Software. Gelfand was a Soviet mathematician who made major contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of numerous awards and honors, including the Order of Lenin and the Wolf Prize, he was a Fellow of the Royal Society and a lifelong academic, serving decades as a professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at the Busch Campus of New Jersey's Rutgers University. He is known for having educated and inspired generations of students through his legendary seminar at Moscow State University. This treatise is devoted to the description and detailed study of the representations of the rotation group of three dimensional space and of the Lorentz group. These groups are of fundamental importance in theoretical physics. The book is also designed for mathematicians studying the representations of Lie groups. For them the book can serve as in introduction to the general theory of representations.

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