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
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.
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