Dressed States Call for Logarithmic Asymptotic Symmetries

Inspired by Wigner's classification of elementary particles as irreducible unitary representations of a spacetime symmetry group, we ask what group can give rise in this way to the quantum states of a particle dressed with clouds of infrared gauge bosons. We show that the answer is given by standard asymptotic symmetries (such as BMS in the gravitational case), supplemented by the logarithmic symmetries identified in arXiv:2305.05436. A corollary is the factorization of the Hilbert space of a dressed particle as a tensor product of the space of `naked' one-particle states with a Hilbert space of soft gauge bosons. The latter cannot be obtained without logarithmic transformations, which are ultimately responsible for the presence of a crucial Heisenberg central extension.