New book on algebraic quantum physics

[A. Neumaier]

TL;DR

The first volume of my treatise on algebraic quantum physics with Dennis Westra is finally out!

I am happy to announce my book

• A. Neumaier and D. Westra, Algebraic Quantum Physics, Vol. 1: Quantum mechanics via Lie algebras, de Gruyter, Berlin 2024.

It features a mathematically rigorous but still physically lucid account of quantum mechanics from the point of view of symmetries, including its foundations.

The book is scheduled to appear in paper form on October 7, 2024. Already now, Google books offers a number of free pages, including among others the table of contents and the introductory chapter with an overview over the whole book.

 

[jedishrfu]

Congratulations!

Writing books, editing books, and proofreading them is hard.

How did you come to write this book? and how long did it take to write, and then get it published?

 

[haushofer]

Congrats! Dennis and I know each other from our time in Groningen. "Mathematically rigorous" sounds a lot like him I hope it will reach a lot of students and researchers!

 

[A. Neumaier]

Congratulations!

Writing books, editing books, and proofreading them is hard.

How did you come to write this book? and how long did it take to write, and then get it published?

Some of this is described in the Preface (visible in Google books). We had a first draft in 2008 (online, much very different from the final version), got in 2017 a contract to publish a revised version. This resulted in a split into two volumes. Finally, we finished the first volume this year. Rough total work load was around 4 hours per written page. A waste of time unless you like to write....
Volume 2 is due in 1 1/2 years, about 75% finished (but only little in final form).

 

[berkeman]

A. Neumaier and D. Westra, Algebraic Quantum Physics, Vol. 1: Quantum mechanics via Lie algebras, de Gruyter, Berlin 2024.

I love this part from the "About this book" section:

Written by a mathematician and a physicist, this book is (like a math book) about precise concepts and exact results in classical mechanics and quantum mechanics, but motivated and discussed (like a physics book) in terms of their physical meaning.

 

[jbergman]

TL;DR Summary: The first volume of my treatise on algebraic quantum physics with Dennis Westra is finally out!

I am happy to announce my book

• A. Neumaier and D. Westra, Algebraic Quantum Physics, Vol. 1: Quantum mechanics via Lie algebras, de Gruyter, Berlin 2024.

It features a mathematically rigorous but still physically lucid account of quantum mechanics from the point of view of symmetries, including its foundations.

The book is scheduled to appear in paper form on October 7, 2024. Already now, Google books offers a number of free pages, including among others the table of contents and the introductory chapter with an overview over the whole book.

Can you say something about the key differences and benefits of the algebraic approach to quantum physics?

 

[A. Neumaier]

Can you say something about the key differences and benefits of the algebraic approach to quantum physics?

1. The use of symmetry (in the form of Lie algebras and Lie groups) organizes the vast material on quantum physics into a form that emphasizes the quantum-classical correspondence.

2. Emphasis is on conceptual understanding rather than on computational techniques. The latter are often simpler in the usual analytic treatment, especially in simple (e.g., exactly solvable) situations and in cases where no high accuracy is required. But this changes once advanced problems must be treated and group theory becomes essential.

3. One works very little with wave functions, which only describe pure states, whereas most realistic systems are in a mixed state (due to temperature and other reasons). Instead, states are described by density operators, which is both more realistic and makes the quantum world look much more like the classical world. For example, density operators have classical (stochastic) limits, while wave functions have no classical analogue.

4. The algebraic approach is adapted to quantum information theory, where algebraic aspects are dominant. As an unexpected consequence, the measurement problem appears in a completely new light.

Reading Chapter 1 (an overview chapter, almost without formulas, available in the Google book link of #1) may give additional aspects.