https://doi.org/10.1140/epjp/s13360-023-03839-z
Regular Article
An internal Lorentz symmetry induces the background Lorentz symmetry in the dissipative dynamics
Instituto de Física, Universidad Autónoma de Puebla, Apartado postal J-48, 72570, Puebla, PUE, Mexico
Received:
28
September
2022
Accepted:
23
February
2023
Published online:
8
March
2023
We show that a dissipative field theory with background Lorentz symmetry underlies the field theory with global 
symmetry constructed on a hyperbolic ring; the theory represents a dissipative model for a bipartite system compound of Klein-Gordon fields with different masses; the infrared limit corresponds to the usual dissipative field theory with a constant dissipative parameter, and with broken background Lorentz symmetry; in the ultraviolet limit the fields behave as free fields with unobservable dissipative effects. In this hyperbolic ring-based formulation, the observables correspond to Hermitian quantities, encoding two real quantities, which are appropriate for describing bipartite system; thus, the Lagrangian is constructed as a Hermitian invariant quantity, and the two real potentials are identified with the subsystem-plus-reservoir system. The potentials can be identified with elliptic and hyperbolic paraboloids by adjusting a real parameter that is interpolating between pure U(1) and pure SO(1, 1) symmetries. At the end we address the problem of constructing a propagator on the hyperbolic ring.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
