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

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

180 submissions , 140 unreviewed
4,598 questions , 1,850 unanswered
5,231 answers , 22,386 comments
1,470 users with positive rep
732 active unimported users
More ...

  Calculation of one-point functions in causal perturbation theory

+ 3 like - 0 dislike
38 views

How are one-point functions evaluated in causal perturbation theory?

I'm not sure where my mistake is in following the standard procedure.

Take the first-order coupling $T_1=\lambda \phi^3$. Within the framework of causal perturbation theory, the corresponding tadpole diagram would be $D^+_m(x_1-x_2):\phi:$ where $D^+_m$ is the positive frequency part of the massive Jordan-Pauli distribution. The singular order is simply that of the given distribution $\omega=-2$, so one can proceed with the splitting procedure trivially:

$$t(x)=R_1-R'_1=D^{+(ret)}_m-D^+_m=D^{+(adv)}_m.$$

For two-point functions, the splitting procedure reproduces the usual Feynman rules if $\omega<0$, and cases where $\omega\geq 0$ are split differently, which avoids UV divergences.

The issue is that the above both does not give a Feynman propagator while having $\omega<0$, yet in the "standard" theory with Feynman rules the tadpole loop would be divergent, suggesting $\omega\geq 0$. Is that discrepancy a feature of the causal theory or have I misconstrued the procedure? In the latter case, what is the procedure to evaluate such diagrams?

This post imported from StackExchange Physics at 2020-03-18 13:31 (UTC), posted by SE-user Quantumness
asked Mar 17 in Theoretical Physics by Quantumness (15 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$\hbar$ysicsOverfl$\varnothing$w
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
...