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Lorentz and permutation invariants of particles

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A theorem of Weyl tells us that the Lorentz (and parity) invariant polynomials in the momenta of n particles are generated by the dot products. We extend this result to include the action of an arbitrary permutation group P ⊂ Sn on the particles, to take account of the quantum-field-theoretic fact that particles can be indistinguishable. Doing so provides a convenient set of variables for describing scattering processes involving identical particles, such as pp → jjj, for which we provide an explicit set of Lorentz and permutation invariant generators. We also address the issues of redundancies among the generators, such as those that arise when n exceeds the spacetime dimension.

This talk is part of the HEP phenomenology joint Cavendish-DAMTP seminar series.

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