• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

174 submissions , 137 unreviewed
4,308 questions , 1,640 unanswered
5,089 answers , 21,602 comments
1,470 users with positive rep
635 active unimported users
More ...

  Fock Space Proof of $(g(x)\phi^4)_2$ Mass Gap?

+ 6 like - 0 dislike

Is there a proof that does not depend on Euclidean methods? Is this a proof? :

$V(g)$ can be written as $P+R$ where $P$ is non-negative and $R$ is $N$-bounded (and hence $(H_0+\lambda P)$-bounded). $H_0+\lambda P$ is essentially self-adjoint by this method. (These are short proofs depending on estimates on the kernels and $\phi < \sqrt N$).

By this theorem, $H_0+\lambda P$ has a gap for small $\lambda$. A gap is stable under the relatively bounded perturbation $\lambda R$, so $H_0+\lambda V$ has a gap for small $\lambda$.

This post imported from StackExchange MathOverflow at 2016-06-08 08:57 (UTC), posted by SE-user Keith McClary
asked Jul 31, 2015 in Theoretical Physics by Keith McClary (30 points) [ no revision ]
retagged Jun 8, 2016

Please log in or register to answer this question.

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights