Looking for a mathematically rigorous definition of a Quantum Field

[LarryS]

TL;DR

Mathematically rigorous definition of a Quantum Field?

I am trying to teach myself QFT. So, that includes understanding the mathematical definition of a Quantum Field. My education is in math, not physics, so for me the theory IS the math. Wikipedia defines a quantum field simply as an operator-valued distribution. But apparently, it does not end there. There are the Wightman Axioms and the Haag-Kastler Axioms and Algebraic QFT.

Is there one true definition of a quantum field? If so, where can I read about it?

Thanks in advance.

 

[martinbn]

How about this one

"Quantum Field Theory: A Tourist Guide for Mathematicians" - Gerald Folland

 

[renormalize]

Is there one true definition of a quantum field? If so, where can I read about it?

You should look at the 4 Wightman axioms W0-W3 and their consequences, as summarized for example here: https://en.wikipedia.org/wiki/Wightman_axioms

 

[Matterwave]

Wikipedia defines a quantum field simply as an operator-valued distribution.

Is there something lacking in mathematical rigor with this definition?

Is there one true definition of a quantum field? If so, where can I read about it?

What kind of thing are you looking for in a "one true definition"?

 

[loop quantum gravity]

You should look at the 4 Wightman axioms W0-W3 and their consequences, as summarized for example here: https://en.wikipedia.org/wiki/Wightman_axioms

But those axioms don't work for 3+1 QFT, at least that's what I understand from Witten's and Jaffa's Millenium prize proposal.
We don't have a constructive QFT for 3+1 dimensions.

 

[jbergman]

I would look at Folland's book or Talagrand's "What is a quantum field theory".