6

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?

michelav
  • 143
  • Related https://physics.stackexchange.com/q/92471/226902 https://physics.stackexchange.com/q/324212/226902 – Quillo Sep 18 '23 at 21:47

2 Answers2

3

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.

DanielC
  • 4,333
1

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

ProphetX
  • 644