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arXiv · 2003.05487

Lorentz and permutation invariants of particles I

Ben Gripaios·Ward Haddadin·Christopher G. Lester
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Abstract

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 $P \subset S_n$ 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 $pp \to jjj$, for which we provide an explicit set of Lorentz and permutation invariant generators.

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Ben Gripaios, Ward Haddadin, Christopher G. Lester. 2020-03-11. Lorentz and permutation invariants of particles I. https://doi.org/10.1088/1751-8121%2Fabe58c

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