Quantum Theory, Groups and Representations: An Introduction
by Peter Woit
Publisher: Columbia University 2014
Number of pages: 396
These notes cover the basics of quantum mechanics, from a point of view emphasizing the role of unitary representations of Lie groups in the foundations of the subject. The approach to this material is simultaneously rather advanced, using crucially some fundamental mathematical structures normally only discussed in graduate mathematics courses, while at the same time trying to do this in as elementary terms as possible.
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In this text the authors introduce the quantum theory understood as a mathematical model describing quantum experiments. This is a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory.
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