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 ...

  (Non)Existence of electroweak symmetry breaking in AQFT

+ 2 like - 0 dislike
718 views

G. Scharf in Gauge Field Theories: Spin One and Spin Two (formerly called Quantum Gauge Theories: A True Ghost Story) shows that there is no symmetry breaking needed to produce massive bosons: One can start with massive gauge fields, then show that in third order of perturbation theory the (broken) Higgs potential is derived, and shifting the field produces the "Higgs mechanism" (pg 167). This does not make sense seeing that on the other hand, other expositions on the topic one starts with massless fields then shows how the Higgs mechanism (by definition) breaks some symmetry to give rise to massive fields.


Considering how electroweak symmetry breaking is energy-dependent, I would think statements concerning existence or properties of the effect need to be supported by renormalization group methods:

In AQFT/causal perturbation theory, what is the Higgs mechanism? Is it just the nonzero VEV of the Higgs field or does it include some sort of "breaking"?
If the classical Lagrangian for the electroweak theory is renormalized (to n-th order) and SSB exists (or does not exist), how would one show it? Does it mean at some scale the finitely renormalized mass $m\left(\rho \ge \Lambda_{EW}\right) =0$ ($\neq 0$)?

asked Oct 16, 2020 in Theoretical Physics by Quantumnessie (90 points) [ no revision ]

1 Answer

+ 2 like - 0 dislike

In causal perturbation theory there is no Higgs mechanism, unless one counts as it the need to introduce a scalar field to produce a causal description for a vector boson.

In traditional perturbation theory if you start with an action that has the Higgs field replaced by one shifted by a constant, you get directly the broken theory.

Thus perturbatively, the label ''broken symmetry'' is just a verbal convention.

Nonperturbatively, the situation may well be different since which symmetries are broken may depend on the boundary conditions considered (energy scale and chemical potential). Different boundary conditions lead to different asymptotic quasiparticle states. Causal perturbation theory almost exclusively considers only the vacuum sector, where this difference does not show up.

answered Oct 16, 2020 by Arnold Neumaier (15,787 points) [ revision history ]

It makes sense that the "Higgs mechanism" and relevant concepts given in Scharf's book could be verbal convention, but does the derivation suffice as rigorous "proof" independent of scale? I heard from another that since causal perturbation theory derives the broken theory, the renormalization group should be used to probe higher energies, but I found that I did not know how to do this or show otherwise (though they may very well be wrong).

The renormalization group only affects the approximation properties of the renormalized series approximation, not the ideal (unknown) nonperturbative solution. The RG is briefly discussed in the second edition of Scharf's book on QED; see also https://www.physicsforums.com/insights/causal-perturbation-theory/

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$\hbar$ysicsOve$\varnothing$flow
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
...