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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ftdoajarticles:oai:doaj.org/article:d22deb57b4b042238585b5e944864703 2024-09-15T18:24:57+00:00 Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space Ion V. Vancea 2017-01-01T00:00:00Z https://doi.org/10.1155/2017/3706870 https://doaj.org/article/d22deb57b4b042238585b5e944864703 EN eng Wiley http://dx.doi.org/10.1155/2017/3706870 https://doaj.org/toc/1687-7357 https://doaj.org/toc/1687-7365 1687-7357 1687-7365 doi:10.1155/2017/3706870 https://doaj.org/article/d22deb57b4b042238585b5e944864703 Advances in High Energy Physics, Vol 2017 (2017) Physics QC1-999 article 2017 ftdoajarticles https://doi.org/10.1155/2017/3706870 2024-08-05T17:48:43Z 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 Directory of Open Access Journals: DOAJ Articles Advances in High Energy Physics 2017 1 14 |
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Directory of Open Access Journals: DOAJ Articles |
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language |
English |
topic |
Physics QC1-999 |
spellingShingle |
Physics QC1-999 Ion V. Vancea Nonequilibrium Dynamics of the σ-Model Modes on the de Sitter Space |
topic_facet |
Physics QC1-999 |
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 |
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 |
Wiley |
publishDate |
2017 |
url |
https://doi.org/10.1155/2017/3706870 https://doaj.org/article/d22deb57b4b042238585b5e944864703 |
genre |
North Pole |
genre_facet |
North Pole |
op_source |
Advances in High Energy Physics, Vol 2017 (2017) |
op_relation |
http://dx.doi.org/10.1155/2017/3706870 https://doaj.org/toc/1687-7357 https://doaj.org/toc/1687-7365 1687-7357 1687-7365 doi:10.1155/2017/3706870 https://doaj.org/article/d22deb57b4b042238585b5e944864703 |
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 |
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1810465348157177856 |