Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915159477321728 |
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| author | Ambruş, Victor E. Chernodub, Maxim N. |
| author_facet | Ambruş, Victor E. Chernodub, Maxim N. |
| contents | We discuss the imaginary-time formalism for field theories in thermal equilibrium in uniformly accelerating frames. We show that under a Wick rotation of Minkowski spacetime, the Rindler event horizon shrinks to a point in a two-dimensional subspace tangential to the acceleration direction and the imaginary time. We demonstrate that the accelerated version of the Kubo-Martin-Schwinger (KMS) condition implies an identification of all spacetime points related by integer-multiple rotations in the tangential subspace about this Euclidean Rindler event-horizon point, with the rotational quanta defined by the thermal acceleration, $α= a/T$. In the Wick-rotated Rindler hyperbolic coordinates, the KMS relations reduce to standard (anti-)periodic boundary conditions in terms of the imaginary proper time (rapidity) coordinate. Our findings pave the way to study, using first-principle lattice simulations, the Hawking-Unruh radiation in geometries with event horizons, phase transitions in accelerating Early Universe and early stages of quark-gluon plasma created in relativistic heavy-ion collisions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03225 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism Ambruş, Victor E. Chernodub, Maxim N. High Energy Physics - Theory Statistical Mechanics General Relativity and Quantum Cosmology High Energy Physics - Lattice We discuss the imaginary-time formalism for field theories in thermal equilibrium in uniformly accelerating frames. We show that under a Wick rotation of Minkowski spacetime, the Rindler event horizon shrinks to a point in a two-dimensional subspace tangential to the acceleration direction and the imaginary time. We demonstrate that the accelerated version of the Kubo-Martin-Schwinger (KMS) condition implies an identification of all spacetime points related by integer-multiple rotations in the tangential subspace about this Euclidean Rindler event-horizon point, with the rotational quanta defined by the thermal acceleration, $α= a/T$. In the Wick-rotated Rindler hyperbolic coordinates, the KMS relations reduce to standard (anti-)periodic boundary conditions in terms of the imaginary proper time (rapidity) coordinate. Our findings pave the way to study, using first-principle lattice simulations, the Hawking-Unruh radiation in geometries with event horizons, phase transitions in accelerating Early Universe and early stages of quark-gluon plasma created in relativistic heavy-ion collisions. |
| title | Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism |
| topic | High Energy Physics - Theory Statistical Mechanics General Relativity and Quantum Cosmology High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2308.03225 |