Entanglement Entropy in the $σ$-Model with the de Sitter Target Space
We derive the formula of the entanglement entropy between the left and right oscillating modes of the $σ$-model with the de Sitter target space. To this end, we study the theory in the \emph{cosmological gauge} in which the non-vanishing components of the metric on the two-dimensional base space are...
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ftdatacite:10.48550/arxiv.1609.02223 2023-05-15T17:39:59+02:00 Entanglement Entropy in the $σ$-Model with the de Sitter Target Space Vancea, Ion V. 2016 https://dx.doi.org/10.48550/arxiv.1609.02223 https://arxiv.org/abs/1609.02223 unknown arXiv https://dx.doi.org/10.1016/j.nuclphysb.2017.09.017 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ High Energy Physics - Theory hep-th General Relativity and Quantum Cosmology gr-qc Mathematical Physics math-ph FOS Physical sciences article-journal Article ScholarlyArticle Text 2016 ftdatacite https://doi.org/10.48550/arxiv.1609.02223 https://doi.org/10.1016/j.nuclphysb.2017.09.017 2022-04-01T11:21:12Z We derive the formula of the entanglement entropy between the left and right oscillating modes of the $σ$-model with the de Sitter target space. To this end, we study the theory in the \emph{cosmological gauge} in which the non-vanishing components of the metric on the two-dimensional base space are functions of the expansion parameter of the de Sitter space. The model is embedded in the causal north pole diamond of the Penrose diagram. We argue that the cosmological gauge is natural to the $σ$-model as it is compatible with the canonical quantization relations. In this gauge, we obtain a new general solution to the equations of motion in terms of time-independent oscillating modes. The constraint structure is adequate for quantization in the Gupta-Bleuler formalism. We construct the space of states as a one-parameter family of Hilbert spaces and give the Bargmann-Fock and Jordan-Schwinger representations of it. Also, we give a simple description of the physical subspace as an infinite product of $\mathcal{D}^{+}_{\frac{1}{2}}$ in the positive discreet series irreducible representations of the $SU(1,1)$ group. We construct the map generated by the Hamiltonian between states at two different values of time and show how it produces the entanglement of left and right excitations. Next, we derive the formula of the entanglement entropy of the reduced density matrix for the ground state acted upon by the Hamiltonian map. Finally, we determine the asymptotic form of the entanglement entropy of a single mode bi-oscillator in the limit of large values of time. : Discussion considerably enriched. References added. This version is consistent with the published article Text North Pole DataCite Metadata Store (German National Library of Science and Technology) North Pole Sitter ENVELOPE(10.986,10.986,64.529,64.529) |
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DataCite Metadata Store (German National Library of Science and Technology) |
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High Energy Physics - Theory hep-th General Relativity and Quantum Cosmology gr-qc Mathematical Physics math-ph FOS Physical sciences |
spellingShingle |
High Energy Physics - Theory hep-th General Relativity and Quantum Cosmology gr-qc Mathematical Physics math-ph FOS Physical sciences Vancea, Ion V. Entanglement Entropy in the $σ$-Model with the de Sitter Target Space |
topic_facet |
High Energy Physics - Theory hep-th General Relativity and Quantum Cosmology gr-qc Mathematical Physics math-ph FOS Physical sciences |
description |
We derive the formula of the entanglement entropy between the left and right oscillating modes of the $σ$-model with the de Sitter target space. To this end, we study the theory in the \emph{cosmological gauge} in which the non-vanishing components of the metric on the two-dimensional base space are functions of the expansion parameter of the de Sitter space. The model is embedded in the causal north pole diamond of the Penrose diagram. We argue that the cosmological gauge is natural to the $σ$-model as it is compatible with the canonical quantization relations. In this gauge, we obtain a new general solution to the equations of motion in terms of time-independent oscillating modes. The constraint structure is adequate for quantization in the Gupta-Bleuler formalism. We construct the space of states as a one-parameter family of Hilbert spaces and give the Bargmann-Fock and Jordan-Schwinger representations of it. Also, we give a simple description of the physical subspace as an infinite product of $\mathcal{D}^{+}_{\frac{1}{2}}$ in the positive discreet series irreducible representations of the $SU(1,1)$ group. We construct the map generated by the Hamiltonian between states at two different values of time and show how it produces the entanglement of left and right excitations. Next, we derive the formula of the entanglement entropy of the reduced density matrix for the ground state acted upon by the Hamiltonian map. Finally, we determine the asymptotic form of the entanglement entropy of a single mode bi-oscillator in the limit of large values of time. : Discussion considerably enriched. References added. This version is consistent with the published article |
format |
Text |
author |
Vancea, Ion V. |
author_facet |
Vancea, Ion V. |
author_sort |
Vancea, Ion V. |
title |
Entanglement Entropy in the $σ$-Model with the de Sitter Target Space |
title_short |
Entanglement Entropy in the $σ$-Model with the de Sitter Target Space |
title_full |
Entanglement Entropy in the $σ$-Model with the de Sitter Target Space |
title_fullStr |
Entanglement Entropy in the $σ$-Model with the de Sitter Target Space |
title_full_unstemmed |
Entanglement Entropy in the $σ$-Model with the de Sitter Target Space |
title_sort |
entanglement entropy in the $σ$-model with the de sitter target space |
publisher |
arXiv |
publishDate |
2016 |
url |
https://dx.doi.org/10.48550/arxiv.1609.02223 https://arxiv.org/abs/1609.02223 |
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://dx.doi.org/10.1016/j.nuclphysb.2017.09.017 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1609.02223 https://doi.org/10.1016/j.nuclphysb.2017.09.017 |
_version_ |
1766140756280475648 |