6
$\begingroup$

I understand that Wightman axioms were defined for scalar quantum field theories. However, what prevents axiomatization of non-scalar quantum field theories, such as gauge theories, even for free field?

Improve this question
$\endgroup$
1

2 Answers 2

Reset to default
3
$\begingroup$

Well, nothing prevents a generalization of Wightman's axioms in case of free gauge theories. This, however, requires in turn a generalization of Hilbert spaces, known as Krein Spaces. The only lucid and thorough presentation I know of is Chapter #10 of BLOT. I hope this boook is available to you.

Improve this answer
$\endgroup$
1
$\begingroup$

As @DanielC Pointed out, Krein spaces are the main ingredient to generalise Wightman axioms to free gauge theories. There is a framework, which you might be looking for: the Strocchi Wightman framework. You can find a detailed description in chapter 7 of the following notes:

https://www-m5.ma.tum.de/foswiki/pub/M5/Allgemeines/WojciechDybalski/Notes-QFT41.pdf

Improve this answer
$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.