Overview

This is a book about representing symmetry in quantum mechanics. The book is on a graduate and/or researcher level and it is written with an attempt to be concise, to respect conceptual clarity and mathematical rigor. The basic structures of quantum mechanics are used to identify the automorphism group of quantum mechanics. The main concept of a symmetry action is defined as a group homomorphism from a given group, the group of symmetries, to the automorphism group of quantum mechanics. The structure of symmetry actions is determined under the assumption that the symmetry group is a Lie group. The Galilei invariance is used to illustrate the general theory by giving a systematic presentation of a Galilei invariant elementary particle. A brief description of the Galilei invariant wave equations is also given.

Full Product Details

Author:   Gianni Cassinelli ,  Ernesto Vito ,  Alberto Levrero ,  Pekka J. Lahti
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 2004
Volume:   654
Dimensions:   Width: 15.50cm , Height: 0.60cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783642061608

ISBN 10:   3642061605
Pages:   111
Publication Date:   03 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Reviews

From the reviews: This slim and carefully written book is devoted to projective representations of continuous groups targeted to the fundamental symmetry group of nonrelativistic quantum mechanics -- the Galilei group. ! The presentation is self-contained and is supplied with necessary background material ! and the list of relevant references. (Alexandr S. Holevo, Zentralblatt MATH, Vol. 1077, 2006) The book is devoted to the study of symmetries in quantum mechanics. ! The book ends with an appendix which collects the necessary mathematical definitions, facts, and theorems needed in the book. In my opinion, the presentation of the material is of the highest quality. Clarity and mathematical rigor make the understanding easy and they make the reading joyful. The book is very much recommended for graduate students and/or researchers of either physics or mathematics interested in the theory of quantum mechanics. (L. Molnar, Publicationes Mathematicae Debrecen, Vol. 68 (1-2), 2006)

From the reviews: This slim and carefully written book is devoted to projective representations of continuous groups targeted to the fundamental symmetry group of nonrelativistic quantum mechanics - the Galilei group. ... The presentation is self-contained and is supplied with necessary background material ... and the list of relevant references. (Alexandr S. Holevo, Zentralblatt MATH, Vol. 1077, 2006) The book is devoted to the study of symmetries in quantum mechanics. ... The book ends with an appendix which collects the necessary mathematical definitions, facts, and theorems needed in the book. In my opinion, the presentation of the material is of the highest quality. Clarity and mathematical rigor make the understanding easy and they make the reading joyful. The book is very much recommended for graduate students and/or researchers of either physics or mathematics interested in the theory of quantum mechanics. (L. Molnar, Publicationes Mathematicae Debrecen, Vol. 68 (1-2), 2006)

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