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

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

136 submissions , 114 unreviewed
3,844 questions , 1,360 unanswered
4,805 answers , 20,346 comments
1,470 users with positive rep
489 active unimported users
More ...

Questions about the equilvalent form of Wick's theorem ?

+ 1 like - 0 dislike
60 views

I have met Wick's theorem first in this book fundamentals of many-body physics (by Wolfgang Nolting) when talk about the perturbation expansion of zero temperature Green's function. Later in the perturbation expansion of finite temperature Green's function I wolud meet this theorem again. In both theories the Wick's theorem is only considered as a operator identity;by which you can transform the time-order product into sums of contraction and normal product.You can see the theorem has nothing to do with the system Hamiltonian that you are caring,no matter the Hamiltonian is quartic (interacting) or quadratic (noninteracting).

Then in this paper Expansion of nonequilibrium Green's functions (by Mathias Wagner ) the author told a general Wick's theorem proved by Danielewicz (Danielewicz,Ann,Phys.152,239(1984)). The general Wick's theorem guarantee the equivalence of the two statements:

  1. Wick's theorem holds exactly (in the form of operator identity);
  2. The operators to be averaged are noninteracting and the initial density matrix is a one-particle density matrix.

I have struggled with the Danielewicz's paper but I still cannot figure out the deep connection between these two statements,can anyboy help me to work out the proof of Danielewicz?Any supporting materials to his proof will also be appreciated.

asked Sep 8 in Theoretical Physics by Kohn (15 points) [ no revision ]

I believe the point about Wick's theorem qua operator identity among creation and annihilation operators versus Wick's theorem qua n-point correlation functions of Gaussian distributions is that the latter come from always quadratic Hamiltonians, which can be quantized using creation and annihilation operators, whereby the correlation function identities follow from the operator identities.

The perturbative expansion is of the interacting theory in terms of the free theory; thus Wick's theorem is always applied to a product of free field operators only - even when using it for the interacting case. 

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).
To avoid this verification in future, please log in or register.




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

Your rights
...