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arXiv · 2205.09468

The Mass Hyperboloid as a Poisson-Lie Group

S. G. Rajeev·Patrizia Vitale
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Abstract

The light cone formalism of a massive scalar field has been shown by Dirac to have many advantages. But it is not manifestly Lorentz invariant. We will show that this is a feature not a bug: Lorentz invariance is indeed a symmetry, but in a different sense defined by Drinfel'd. The key idea is that the mass shell (mass hyperboloid) is a Poisson-Lie group: there is a non-abelian group multiplication and non-zero Poisson brackets between components of four-momentum. Rotations form the dual group of the hyperboloid in the sense of Drinfel'd. Infinitesimal Lorentz transformations form a Lie bi-algebra.

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S. G. Rajeev, Patrizia Vitale. 2022-05-19. The Mass Hyperboloid as a Poisson-Lie Group. https://arxiv.org/abs/2205.09468

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