• 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.


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

143 submissions , 120 unreviewed
3,899 questions , 1,377 unanswered
4,834 answers , 20,491 comments
1,470 users with positive rep
494 active unimported users
More ...

  Assumptions of the Coleman-Mandula Theorem

+ 6 like - 0 dislike

In the original paper All Possible Symmetries of the S-Matrix, by S. Coleman and J. Mandula, they prove their famous 'no go' theorem regarding the possible extensions of Poincaré symmetry. The loophole that allows for supersymmetry is their assumption that the generators are bosonic, as it is often said in modern introductory courses to SUSY. But I have not been able to pinpoint this precise statement in their original paper.

enter image description here

Could the fifth requirement be that assumption, that the generators are bosonic? If so, I do not see why demanding that the generators be integral operators is equivalent to demanding they be bosonic, as opposed to fermionic generators with spinor indices which satisfy anti-commutation relations. Perhaps the statement, often quoted in lectures, that the assumption is that they are 'bosonic,' is a gross simplification, or inaccuracy?

This post imported from StackExchange Physics at 2014-03-31 16:04 (UCT), posted by SE-user JamalS
asked Mar 31, 2014 in Theoretical Physics by JamalS (885 points) [ no revision ]

1 Answer

+ 3 like - 0 dislike

It looks like this loophole is not explicitly discussed in the "axioms", but it is mentioned in the paragraph before equation (2) which I copy here:

A symmetry transformation is said to be an internal symmetry transformation if it commutes with P. This implies that it acts only on particle-type indices, and has no matrix elements between particles of different four-momentum or different spin. A group composed of such transformations is called an internal symmetry group.

By demanding that commutators vanish, they exclude SUSY, since not all the supercharges commute with all Poincare generators. See for example equation (2.53) in [1].

A very nice discussion regarding the Coleman Mandula theorem can also be found in [2].

Hope this helps!



[2]Weinberg’s QFT book,Vol. III, chapter 24.B

This post imported from StackExchange Physics at 2014-03-31 16:04 (UCT), posted by SE-user Heterotic
answered Mar 31, 2014 by Heterotic (525 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:
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