Good books on the group theory of quantum mechanics

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Discussion Overview

The discussion centers around recommendations for books on the group theory of quantum mechanics, with a particular emphasis on resources that can aid in understanding quantum electrodynamics. Participants share their backgrounds and specific interests in the topic.

Discussion Character

  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant suggests Greiner & Müller, "Quantum Mechanics: Symmetries," as a good starting point.
  • Another participant recommends S. Sternberg's "Group Theory and Physics," noting its modern presentation and comprehensible explanation of Young diagrams in physics.
  • A different participant mentions Ballentine's "Quantum Mechanics" and Weinberg's "Lectures on Quantum Mechanics" for a treatment of the Galilei group, and suggests Weinberg's "The Quantum Theory of Fields" for the relativistic case.
  • Additionally, a more general book on (Poincare) symmetry in physics, "Relativity, Groups, Particles," is recommended for those seeking broader context.

Areas of Agreement / Disagreement

Participants present multiple recommendations without expressing disagreement, indicating a variety of perspectives on suitable resources for studying group theory in quantum mechanics.

Contextual Notes

Some participants express challenges in understanding certain texts, such as Weinberg's "The Quantum Theory of Fields," suggesting that the complexity of the material may vary significantly among different books.

Who May Find This Useful

This discussion may be useful for individuals with a background in physics or engineering who are seeking to deepen their understanding of quantum mechanics through the lens of group theory.

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Hello
I'm looking for good books on the group theory of quantum mechanics. I have a BS in Physics, MS in Electrical Engineering and decades of work experience in building lasers, and R&D in laser systems, optics & infrared sensing systems.

My main goal is to study & understand quantum electrodynamics.

Thanks
 
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I like S. Sternberg's "Group Theory and Physics". In contrast to the authors of most other books on group theory as applied to physics, he isn't a physicist but a mathematician. This has the effect that the presentation of the methods is much more modern and up to date than what can be found in other books. For example, it is the only book where I found a comprehensible explanation of the uses of Young diagrams in physics.
 
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A good treatment of the Galilei group in quantum theory can be found in Ballentine, Quantum Mechanics and Weinberg, Lectures on Quantum Mechanis. For the relativistic case I recommend Weinberg, The quantum theory of fields.

A more introductory book, not restricted to quantum theory but more general about (Poincare) symmetry in physics is Relativity, Groups, Particles.
 
Thanks folks, I'll look into these suggestions.

PS: I have Weinberg, The quantum theory of fields Volume 1. I've read the first 80 pages three times- and then I'm lost.
 

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