EAN: 9783319646107

QUANTUM THEORY GROUPS AND REPRESENTATIONS - PET...

This text systematically presents the basics of quantum mechanics  emphasizing the role of Lie
groups  Lie algebras  and their unitary representations. The mathematical structure of the
subject is brought to the fore  intentionally avoiding significant overlap with material from
standard physics courses in quantum mechanics and quantum field theory. The level of
presentation is attractive to mathematics students looking to learn about both quantum
mechanics and representation theory  while also appealing to physics students who would like to
know more about the mathematics underlying the subject. This text showcases the numerous
differences between typical mathematical and physical treatments of the subject. The latter
portions of the book focus on central mathematical objects that occur in the Standard Model of
particle physics  underlining the deep and intimate connections between mathematics and the
physical world. While an elementary physics course of some kind would be helpful to the reader
no specific background in physics is assumed  making this book accessible to students with a
grounding in multivariable calculus and linear algebra. Many exercises are provided to develop
the reader's understanding of and facility in quantum-theoretical concepts and calculations.

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