# Coleman-Mandula theorem in mathematical language

+ 5 like - 0 dislike
278 views

Every supersymmetry text starts off mentioning the Coleman-Mandula theorem. Often it is introduced using rather colloquial terminology. I was wondering if anyone knew a precise mathematical formulation of the theorem.

This post imported from StackExchange Physics at 2014-08-11 14:58 (UCT), posted by SE-user SWV
For everyone interested, here's a link to the original paper: prola.aps.org/abstract/PR/v159/i5/p1251_1

This post imported from StackExchange Physics at 2014-08-11 14:58 (UCT), posted by SE-user Vibert
Weinberg Volume 3 has a derivation of the theorem in the first (or maybe second) chapter.

This post imported from StackExchange Physics at 2014-08-11 14:58 (UCT), posted by SE-user Prahar

This post imported from StackExchange Physics at 2014-08-11 14:58 (UCT), posted by SE-user Sanath Devalapurkar
I find that this paper is particularly accessible and constitutes a nice derivation of the individual elements of the proof. ippp.dur.ac.uk/~busbridge/files/documents/CMtheorem.pdf

This post imported from StackExchange Physics at 2014-08-11 14:58 (UCT), posted by SE-user Autolatry

+ 4 like - 0 dislike

See http://arxiv.org/pdf/hep-th/9605147v1.pdf. Most of the following is verbatim from there.

Theorem: With the following assumptions: $G$ is a group of symmetries of the $S$-matrix $\mathscr{S}$$G$ contains a subgroup $\mathcal{P}^\prime_0$ that is locally isomorphic to $\mathcal{P}(r,1)$ for $r\geq3$; all particle types correspond to positive-energy time-like representations of the universal covering group of $\mathcal{P}^\prime_0$; the number of particle types is finite; at least locally, $G$ is generated by generators represented in the one-particle space $\mathcal{H}^{(1)}$ by (generalized) integral operators in momentum space, with distributions as kernels; the amplitudes for elastic scattering of two particles do not vanish identically; and the scattering amplitudes are regular functions of the momenta, and the amplitudes for scattering between two-particle states are analytic functions in some neighborhood of the physical region, we can state that $G$ is isomorphic to the direct product of $\mathcal{P}^\prime_0$ and the direct product of some internal symmetry group.

See the linked paper for the proof of the statement, if needed.

answered Sep 12, 2014 by (285 points)

 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): Email me at this address if my answer is selected or commented on: 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$\hbar$ysicsOv$\varnothing$rflowThen 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.