https://doi.org/10.1140/epjc/s10052-020-8161-x
Regular Article - Theoretical Physics
Hyperbolic ring based formulation for thermo field dynamics, quantum dissipation, entanglement, and holography
1
Instituto de Física, Universidad Autónoma de Puebla, Apartado postal J-48, 72570, Puebla Pue, Mexico
2
Facultad de Ciencias, Universidad Autónoma de San Luis Potosí Campus Pedregal, Av. Parque Chapultepec 1610, Col. Privadas del Pedregal, 78217, San Luis Potosí, SLP, Mexico
3
Lux Systems, C.P. 27010, Blvrd Independencia 2002, Colonia Estrella, Torreón, Coah, Mexico
* e-mail: jasel.berra@uaslp.mx
Received:
7
April
2020
Accepted:
16
June
2020
Published online:
3
July
2020
The classical and quantum formulations for open systems related to dissipative dynamics are constructed on a complex hyperbolic ring, following universal symmetry principles, and considering the double thermal fields approach for modeling the system of interest, and the environment. The hyperbolic rotations are revealed as an underlying internal symmetry for the dissipative dynamics, and a chemical potential is identified as conjugate variable to the charge operator, and thus a grand partition function is constructed. As opposed to the standard scheme, there are not patologies associated with the existence of many unitarity inequivalent representations on the hyperbolic ring, since the whole of the dissipative quantum dynamics is realized by choosing only one representation of the field commutation relations. Entanglement entropy operators for the subsystem of interest and the environment, are constructed as a tool for study the entanglement generated from the dissipation. The holographic perspectives of our results are discussed.
© The Author(s), 2020
