Discovering Sparse Representations of Lie Groups with Machine Learning

Roy T. Forestano, Konstantin T. Matchev, Katia Matcheva, Alexander Roman, Eyup B. Unlu +1 more
2/10/2023
hep-phcs.LGmath-ph

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Abstract

Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and to obtain the corresponding algebras of generators. In this letter, we extend this technique to derive sparse representations of arbitrary Lie algebras. We show that our method reproduces the canonical (sparse) representations of the generators of the Lorentz group, as well as the $U(n)$ and $SU(n)$ families of Lie groups. This approach is completely general and can be used to find the infinitesimal generators for any Lie group.

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Cite this paper

@article{forestano2023discovering,
  title  = {Discovering Sparse Representations of Lie Groups with Machine Learning},
  author = {Roy T. Forestano and Konstantin T. Matchev and Katia Matcheva and Alexander Roman and Eyup B. Unlu and Sarunas Verner},
  year   = {2023},
  eprint = {2302.05383},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2302.05383v1}
}

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