Abstract
We show that a dissipative field theory with background Lorentz symmetry underlies the field theory with global \(U(1)\times SO(1,1)\) 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 \(U(1)\times SO(1,1)\) 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.
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Acknowledgements
This work was supported by the Sistema Nacional de Investigadores (México). Juarez-Dominguez acknowledges the financial support by CONACYT (Mexico) under Grant No. CB-2014-01/240781.
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Cartas-Fuentevilla, R., Juarez-Dominguez, A.J.C. An internal Lorentz symmetry induces the background Lorentz symmetry in the dissipative dynamics. Eur. Phys. J. Plus 138, 217 (2023). https://doi.org/10.1140/epjp/s13360-023-03839-z
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DOI: https://doi.org/10.1140/epjp/s13360-023-03839-z