Vacuum state Lorentz invariance

[Gvido_Anselmi]

Hi everybody!
Why we don't have to prove Lorentz invariance of the Vacuum state in QFT?
This fact is quite obvious in QED and follows from Lorentz invariance of electric charges.
But in general case?
I don't know, but it seems to me this fact is not so obvious as it treated.

 

[atyy]

It is proved in rigourous relativistic quantum field theory by verifying that the construction satisfies conditions such as the Osterwalder-Schrader conditions.

So far, rigourous relativistic QFTs have only been constructed in 1+1D and 2+1d. The usual quantum field theories like QED etc are not rigourous.

 

[Gvido_Anselmi]

It is proved in rigourous relativistic quantum field theory by verifying that the construction satisfies conditions such as the Osterwalder-Schrader conditions.

So far, rigourous relativistic QFTs have only been constructed in 1+1D and 2+1d. The usual quantum field theories like QED etc are not rigourous.

Thank you for your answer! Where can I read about it?

 

[atyy]

http://ncatlab.org/nlab/show/Wightman+axioms
http://ncatlab.org/nlab/show/Osterwalder-Schrader+theorem

http://rivasseau.com/resources/book.pdf
From perturbative to constructive Renormalization
Vincent Rivasseau

https://www.amazon.com/dp/1107005094/?tag=pfamazon01-20
Quantum Mechanics and Quantum Field Theory: A Mathematical Primer
Jonathan Dimock

http://www.claymath.org/millennium-problems/yang–mills-and-mass-gap

 

[Gvido_Anselmi]

http://ncatlab.org/nlab/show/Wightman+axioms
http://ncatlab.org/nlab/show/Osterwalder-Schrader+theorem

http://rivasseau.com/resources/book.pdf
From perturbative to constructive Renormalization
Vincent Rivasseau

https://www.amazon.com/dp/1107005094/?tag=pfamazon01-20
Quantum Mechanics and Quantum Field Theory: A Mathematical Primer
Jonathan Dimock

Thank you, I will study these texts. And how do you like Bogoliubov's books on axiomatic QFT?
Can I also ask for your opinion on this paper? http://arxiv.org/pdf/1209.0209v2.pdf

 

[atyy]

Thank you, I will study these texts. And how do you like Bogoliubov's books on axiomatic QFT?
Can I also ask for your opinion on this paper? http://arxiv.org/pdf/1209.0209v2.pdf

I haven't read Bogoliubov's book, and I am not competent to comment on Bednorz's paper. But I found very interesting comments on it at http://www.fuw.edu.pl/~abednorz/riv/rev.html.

 

[Gvido_Anselmi]

Ok, then I will better follow your recommendations in literature ))

 

[atyy]

Ok, then I will better follow your recommendations in literature ))

Well, the comments of the referees don't seem to disagree that Bednorz's work is correct. The only dispute is about its novelty. So it seems Bednorz's paper is worth studying. I think the main limitation of the proof is that it is perturbative, as Bednorz mentions in his abstract, so it assumes the theory exists. In contrast, the references I gave do construct the theory.

 

[Gvido_Anselmi]

Well, the comments of the referees don't seem to disagree that Bednorz's work is correct. The only dispute is about its novelty. So it seems Bednorz's paper is worth studying. I think the main limitation of the proof is that it is perturbative, as Bednorz mentions in his abstract, so it assumes the theory exists. In contrast, the references I gave do construct the theory.

Thank you very much. Quite possible it worth studying. But it seems to me quite strange in some ways. It's very different from QFT to which I am accustomed. So my decision is that following your recommendations will be more usefull now.