Completing Multiparticle Representations of the Poincar\'e Group

Open Access

Completing Multiparticle Representations of the Poincaré Group

Csaba Csáki, Sungwoo Hong, Yuri Shirman, Ofri Telem, and John Terning

Phys. Rev. Lett. 127, 041601 – Published 23 July 2021

Abstract

We extend the definition of asymptotic multiparticle states of the $S$ -matrix beyond the tensor products of one-particle states. We identify new quantum numbers called pairwise helicities, or $q_{i j}$ , associated with asymptotically separated pairs of particles. We first treat all single particles and particle pairs independently, allowing us to generalize the Wigner construction, and ultimately projecting onto the physical states. Our states reduce to tensor product states for vanishing $q_{i j}$ , while for vanishing spins they reproduce Zwanziger’s scalar dyon states. This construction yields the correct asymptotic states for the scattering of electric and magnetic charges, with pairwise helicity identified as $q_{i j} = e_{i} g_{j} - e_{j} g_{i}$ .

Received 4 January 2021
Revised 10 June 2021
Accepted 22 June 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.041601

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particle interactions Scattering amplitudes

Magnetic monopoles

Lorentz symmetry

Group theory

Particles & Fields

Authors & Affiliations

Csaba Csáki¹, Sungwoo Hong^2,3, Yuri Shirman ⁴, Ofri Telem ^5,6, and John Terning ⁷

¹Department of Physics, LEPP, Cornell University, Ithaca, New York 14853, USA
²Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA
³Argonne National Laboratory, Lemont, Illinois 60439, USA
⁴Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
⁵Theory Group, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁶Berkeley Center for Theoretical Physics, University of California, Berkeley, California 94720, USA
⁷QMAP, Department of Physics, University of California, Davis, California 95616, USA