Lectures on quantum theory, by Chris Isham

[Fredrik]

This is an excellent book, so I'm surprised it's only been mentioned once before in the science book forum. It deserves a lot more attention than that, so I thought I'd at least post a recommendation. The full title is "Lectures on quantum theory: mathematical and structural foundations". If you have already taken a QM class and want to understand the foundations better, this is a very good place to start.

This is supposed to be a fairly easy book, so he has chosen not to include the difficult mathematics (advanced functional analysis, how to find irreducible representations of symmetry groups, etc.). But he always let's you know what he's leaving out, so that you know what to look for if you want to know more. It's written for undergraduates, but I'm sure a lot of graduate students would find it useful too.

It contains a very good discussion about state preparation and measurements, and about some of the interpretational issues. He doesn't go into detail about the various attempts to interpret state vectors as representing objective properties of physical systems, but he talks a lot about "realism" vs "anti-realism". The book also contains an introduction to quantum logic at the end.

It contains a small number of exercises, with complete solutions.

 

[George Jones]

I love this book.

In my head, I referred to this book in quite a few responses to posts in this forum, but, unfortunately, only one response made it from my head to the keyboard.

 

[peterphys]

With reference to fourth anti-realist interpo in section 5.1.1:
... a quantum state should not be associated with an individual system; rather, it
refers only to a collection, or ‘ensemble’ copies of the system...
How to represent this ensemble of system matematically?
Doesn't |psi> represent an individual system?

 

[Fredrik]

That's also possible. (It's option #1 on the list). We don't know what the state vector actually represents, since experiments can only tell us how accurate the theory's predictions are. The predictions are the same regardless of which option on the list is correct.

If we choose option 1, the many-worlds interpretation or something very much like it appears inevitable, because the formalism doesn't contain any indication that one of the possibilities is more real than the others. If we choose option 4, we're essentially saying that even though QM makes excellent predictions about probabilities of results of experiments, it isn't telling us anything about what actually happens to physical systems. It's just a set of rules that tells us how to calculate probabilities of possibilities.

 

[rezeew]

As a scientist familiar with quantum theory, I can say that Chris Isham's book on quantum theory is indeed an excellent resource for understanding the mathematical and structural foundations of this complex field. It is surprising that it has not received more attention in the science book forum, as it provides a valuable and accessible introduction to the subject.

I appreciate that Isham has chosen to focus on the core concepts and principles of quantum theory rather than getting bogged down in advanced mathematics. This makes the book accessible to a wider audience, including undergraduates and graduate students who may be looking to deepen their understanding of the foundations of quantum theory.

I also appreciate that Isham acknowledges the limitations of his book and points readers towards further resources for those who want to delve deeper into specific topics. This approach allows readers to tailor their learning and pursue areas of interest in more detail.

The book's discussion on state preparation and measurements, as well as the interpretational issues surrounding quantum theory, is particularly valuable. Isham's treatment of realism and anti-realism provides a thought-provoking perspective on the nature of quantum systems and their properties.

The inclusion of exercises with complete solutions is a great addition, as it allows readers to test their understanding and further solidify their knowledge.

Overall, I highly recommend Chris Isham's "Lectures on quantum theory" to anyone looking to gain a deeper understanding of the mathematical and structural foundations of this fascinating field. It is a valuable resource for both undergraduates and graduate students, and I believe it deserves more attention in the science book forum.