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Advances in High Energy Physics
Volume 2017 (2017), Article ID 3706870, 14 pages
Research Article

Nonequilibrium Dynamics of the -Model Modes on the de Sitter Space

Grupo de Física Teórica e Matemática Física, Departamento de Física, Universidade Federal Rural do Rio de Janeiro, Cx. Postal 23851, BR 465 Km 7, 23890-000 Seropédica, RJ, Brazil

Correspondence should be addressed to Ion V. Vancea; rb.jrrfu@aecnavnoi

Received 27 April 2017; Revised 9 July 2017; Accepted 2 August 2017; Published 29 August 2017

Academic Editor: Shi-Hai Dong

Copyright © 2017 Ion V. Vancea. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


The two-dimensional -model with the de Sitter target space is locally canonic in the north pole diamond of the Penrose diagram in the cosmological gauge. The left and right moving modes on the cylindrical base space are entangled among themselves and interact with the de Sitter metric. Firstly, we show that the untangled oscillators can be obtained from the entangled operators by applying a set of Bogoliubov transformations constrained by the requirement that the partial evolution generator be diagonal. Secondly, we determine the nonequilibrium dynamics of the untangled modes in the nonequilibrium thermofield dynamics formalism. The thermal modes are represented as thermal doublet oscillators that satisfy partial evolution equations of Heisenberg-type. From these we compute the local free one-body propagator of an arbitrary mode between two times. Thirdly, we discuss the field representation of the thermal modes. We show that there is a set of thermal doublet fields that satisfy the equal time canonical commutation relations, are solutions to the -model equations of motion, and can be decomposed in terms of thermal doublet oscillators. Finally, we construct a local partial evolution functional of Hamilton-like form for the thermal doublet fields.