• 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.


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


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,075 questions , 2,226 unanswered
5,348 answers , 22,757 comments
1,470 users with positive rep
818 active unimported users
More ...

  Dirac's Equation derivation from the Standard model?

+ 2 like - 0 dislike

Historically, the reconciliation of quantum mechanics and relativity led to the single-particle Dirac’s equation
$$(i\gamma^\mu\partial_\mu – m)\psi = 0.$$
This last allowed to explain correctly the fine structure of the spectrum of hydrogen atom and to predict the existence of anti-particles. However, it also lead to inconsistencies: negative energy states and a non-positive-definite probability density. These inconsistencies motivated in turn the development of a full relativistic quantum theory of fields: QFT. However, bound states - such as the hydrogen atom - are not easily treated within QFTs. The Bethe-Salpeter equation is the most orthodox tool for discussing the relativistic two-body problem in QFT. In particular, the hydrogen atom is usually treated in an approximation where the proton is treated as an external Coulomb field. 

Given all this, it seems reasonable to expect something like the original Dirac Equation with a Coulomb potential to be recoverable from the standard model through the Bethe-Salpeter equation or analogue methods. As far as I understand, this is in the same spirit of what happens in chapters 13.6 and 14 of Weinber Vol 1. However, I am unsure my reading is correct.

In summary, is my exposition correct? Is the expectation of such a derivation justified? Has it already been done and if so where? And with what subtleties?

asked Dec 14, 2022 in Theoretical Physics by Taytak [ no revision ]

Couldn't you just sum over lowest order diagrams in perturbative QED? 


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:
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