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  Coleman-Mandula theorem in mathematical language

+ 5 like - 0 dislike

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
asked Jan 21, 2014 in Theoretical Physics by SWV (60 points) [ no revision ]
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
Possible answer: physics.stackexchange.com/q/3645

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

1 Answer

+ 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 SDevalapurkar (285 points) [ revision history ]

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