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
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Branch cuts in two-point function

+ 4 like - 0 dislike
2227 views

The propagator of a QFT is known to have a branch cut as a function of the (complex) external momentum. The branch point (as done by, say, Peskin & Schroeder in eqn.7.19 section 7.1) is identified as the root of the argument of the logarithmic piece. Is this not a scheme dependent piece? At least, at the outset it looks so and it is also the same that one gets under dimensional regularization. Is there a general argument to prove that it is scheme independent?

This post imported from StackExchange Physics at 2014-04-21 16:24 (UCT), posted by SE-user MadKal
asked Apr 19, 2014 in Theoretical Physics by MadKal (20 points) [ no revision ]
retagged Apr 21, 2014
It is not clear what you mean by this... the exact propagator function (along with all other Green functions in QFT) is renormalization scheme independent. Therefore, any singularities such as cuts and poles would also be scheme independent.

This post imported from StackExchange Physics at 2014-04-21 16:24 (UCT), posted by SE-user QuantumDot
I agree with your statement. That was why eqn.7.19 in section 7.1 of Peskin & Schroeder confused me. The log[(1-x)m_0^2+...] term that determines the location of branch cut is part of the finite pieces of the subtractions - which are the scheme dependent pieces. My only question was whether there are some general arguments to show that this piece or the location of the branch cuts therein are scheme independent. I have to look at what is suggested below.

This post imported from StackExchange Physics at 2014-04-21 16:24 (UCT), posted by SE-user MadKal

1 Answer

+ 1 like - 0 dislike

The logs that you get at one loop are scheme independent pretty much like the beta function at one loop is. There is a nice and neat discussion about it on the second volume of Weinberg.

This post imported from StackExchange Physics at 2014-04-21 16:24 (UCT), posted by SE-user TwoBs
answered Apr 19, 2014 by TwoBs (315 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$\hbar$ysic$\varnothing$Overflow
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
...