Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space
The two-dimensional σ-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...
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fthindawi:oai:hindawi.com:10.1155/2017/3706870 2023-05-15T17:39:54+02:00 Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space Ion V. Vancea 2017 https://doi.org/10.1155/2017/3706870 en eng Advances in High Energy Physics https://doi.org/10.1155/2017/3706870 Copyright © 2017 Ion V. Vancea. Research Article 2017 fthindawi https://doi.org/10.1155/2017/3706870 2019-05-26T08:56:06Z The two-dimensional σ-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 σ-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. Article in Journal/Newspaper North Pole Hindawi Publishing Corporation North Pole Sitter ENVELOPE(10.986,10.986,64.529,64.529) Advances in High Energy Physics 2017 1 14 |
institution |
Open Polar |
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Hindawi Publishing Corporation |
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fthindawi |
language |
English |
description |
The two-dimensional σ-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 σ-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. |
format |
Article in Journal/Newspaper |
author |
Ion V. Vancea |
spellingShingle |
Ion V. Vancea Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space |
author_facet |
Ion V. Vancea |
author_sort |
Ion V. Vancea |
title |
Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space |
title_short |
Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space |
title_full |
Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space |
title_fullStr |
Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space |
title_full_unstemmed |
Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space |
title_sort |
nonequilibrium dynamics of the σ-model modes on the de sitter space |
publisher |
Advances in High Energy Physics |
publishDate |
2017 |
url |
https://doi.org/10.1155/2017/3706870 |
long_lat |
ENVELOPE(10.986,10.986,64.529,64.529) |
geographic |
North Pole Sitter |
geographic_facet |
North Pole Sitter |
genre |
North Pole |
genre_facet |
North Pole |
op_relation |
https://doi.org/10.1155/2017/3706870 |
op_rights |
Copyright © 2017 Ion V. Vancea. |
op_doi |
https://doi.org/10.1155/2017/3706870 |
container_title |
Advances in High Energy Physics |
container_volume |
2017 |
container_start_page |
1 |
op_container_end_page |
14 |
_version_ |
1766140664588795904 |