Tachyons and Representations of Sp(2,R)

Lacking in the mathematical physics literature is a detailed treatment of tachyonic representations of the Poincaré group along lines similar to that for its real mass, positive and negative energy representations. Such representations Wigner did not consider in any detail in his 1939 paper on the unitary representations of the inhomogeneous Lorentz group (Wigner, Ann Math 40:149–204, 1939), and Bargmann and Wigner in their paper on the group theoretical classification of relativistic wave equations did not consider them either because “they are . . . unlikely to have a simple physical interpretation” (Bargmann and Wigner, Proc Nat Acad Sci (USA) 34(5):211–223, 1948). Here we make a detailed study of tachyonic representations of the Poincaré group in four space-time dimensions and we describe some of our results here. In particular, we relate tachyonic representations of the Poincaré group to representations of the anti-de Sitter group, in a way analogous to the way in which positive energy, real mass representations of the Poincaré group are related to unitary principal series representations of the de Sitter group via group contraction and deformation.

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Work Title Tachyons and Representations of Sp(2,R)
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Open Access
Creators
  1. Patrick Moylan
Keyword
  1. Tachyons
  2. Representation theory
  3. Poincaré group
  4. de Sitter groups
License In Copyright (Rights Reserved)
Work Type Part Of Book
Publisher
  1. Quantum Theory and Symmetries. CRM Series in Mathematical Physics. Springer, Cham.
Publication Date August 8, 2020
Publisher Identifier (DOI)
  1. https://doi.org/10.1007/978-3-030-55777-5_12
Deposited February 17, 2023

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Version 1
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  • Created
  • Added tachyons_and_reps_of_so_2_3__moylan_CRNS_Montreal_2020.pdf
  • Added Creator Patrick Moylan
  • Published
  • Updated Keyword, Subtitle, Publisher, and 2 more Show Changes
    Keyword
    • Tachyons, Representation theory, Poincaré group, de Sitter groups
    Subtitle
    • M. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in Mathematical Physics,, Springer Nature, Switzerland, 2021
    Publisher
    • CRM Series in Mathematical Physics,, Springer Nature, Switzerland, 2021
    • Quantum Theory and Symmetries. CRM Series in Mathematical Physics. Springer, Cham.
    Publisher Identifier (DOI)
    • https://doi.org/10.1007/978-3-030-55777-5_12
    Publication Date
    • 2021-05-01
    • 2020-08-08