Quantcast
  • 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.

News

PO is now at the Physics Department of Bielefeld University!

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

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,786 comments
1,470 users with positive rep
820 active unimported users
More ...

  Converse and generalization of Wick's theorem

+ 3 like - 0 dislike
1169 views

Apologies if this comes off as too trivial. The question stems from my reading of Papadodimas and Raju's paper, 'An Infalling Observer in AdS/CFT' (hep-th/1211.6767), in which they introduce the notion of a 'generalized free field'. The n-point functions of such a field may be written as the sum over all possible pairings of n objects, with each pair corresponding to a 2-point function, up to leading order in some parameter 1/N (unrelated to the usual usage of as the number of flavors).

I was thus led to wonder whether it is possible to have distributions other than the Guassian in, say, a 0-dimensional QFT, which also satisfy Wick's theorem. Additionally, are there distributions (perhaps with the square in the exponent of the Gaussian replaced by an mth power) for which the n-point functions are given by a sum over all possible m-groupings of n objects, so that perturbation theory around such backgrounds would involve dealing with Feynman hypergraphs?

I suppose a combinatorial proof of Wick's theorem can help clarify how far we can go in this direction, but unfortunately, I haven't been able to come up with one.

asked Jul 12, 2014 in Theoretical Physics by Arpan Saha (50 points) [ revision history ]

1 Answer

+ 4 like - 0 dislike

Wick's theorem for boson fields is fully equivalent to the Gaussian assumption.

However, there is also a Wick's theorem for generalized free fermion fields with a given 2-point function, with slightly different signs. These are not Gaussians, but also qualify as generalized free field, as the free fermion field is a special case.

There are no other instances of Wick's theorem. This can be seen by deriving a functional differential equation for the cumulant generating function.

answered Jul 12, 2014 by Arnold Neumaier (15,787 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOverflo$\varnothing$
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




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

Your rights
...