On A. D. Sakharov’s Hypothesis of Cosmological Transitions with Changes in the Signature of the Metric
The paper discusses possible consequences of A. D. Sakharov’s hypothesis of cosmological transitions with changes in the signature of the metric, based on the path integral approach. This hypothesis raises a number of mathematical and philosophical questions. Mathematical questions concern the defin...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-05-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/7/5/151 |
| _version_ | 1797533855341608960 |
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| author | Tatyana P. Shestakova |
| author_facet | Tatyana P. Shestakova |
| author_sort | Tatyana P. Shestakova |
| collection | DOAJ |
| description | The paper discusses possible consequences of A. D. Sakharov’s hypothesis of cosmological transitions with changes in the signature of the metric, based on the path integral approach. This hypothesis raises a number of mathematical and philosophical questions. Mathematical questions concern the definition of the path integral to include integration over spacetime regions with different signatures of the metric. One possible way to describe the changes in the signature is to admit time and space coordinates to be purely imaginary. It may look like a generalization of what we have in the case of pseudo-Riemannian manifolds with a non-trivial topology. The signature in these regions can be fixed by special gauge conditions on components of the metric tensor. The problem is what boundary conditions should be imposed on the boundaries of these regions and how they should be taken into account in the definition of the path integral. The philosophical question is what distinguishes the time coordinate among other coordinates but the sign of the corresponding principal value of the metric tensor. In particular, there is an attempt in speculating how the existence of the regions with different signature can affect the evolution of the Universe. |
| first_indexed | 2024-03-10T11:20:37Z |
| format | Article |
| id | doaj.art-04547976127e4375bbad4959614cb9c7 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-10T11:20:37Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-04547976127e4375bbad4959614cb9c72023-11-21T20:00:21ZengMDPI AGUniverse2218-19972021-05-017515110.3390/universe7050151On A. D. Sakharov’s Hypothesis of Cosmological Transitions with Changes in the Signature of the MetricTatyana P. Shestakova0Department of Theoretical and Computational Physics, Southern Federal University, Sorge St. 5, 344090 Rostov-on-Don, RussiaThe paper discusses possible consequences of A. D. Sakharov’s hypothesis of cosmological transitions with changes in the signature of the metric, based on the path integral approach. This hypothesis raises a number of mathematical and philosophical questions. Mathematical questions concern the definition of the path integral to include integration over spacetime regions with different signatures of the metric. One possible way to describe the changes in the signature is to admit time and space coordinates to be purely imaginary. It may look like a generalization of what we have in the case of pseudo-Riemannian manifolds with a non-trivial topology. The signature in these regions can be fixed by special gauge conditions on components of the metric tensor. The problem is what boundary conditions should be imposed on the boundaries of these regions and how they should be taken into account in the definition of the path integral. The philosophical question is what distinguishes the time coordinate among other coordinates but the sign of the corresponding principal value of the metric tensor. In particular, there is an attempt in speculating how the existence of the regions with different signature can affect the evolution of the Universe.https://www.mdpi.com/2218-1997/7/5/151A. D. Sakharovmetric signaturepath integral quantizationunitary evolution |
| spellingShingle | Tatyana P. Shestakova On A. D. Sakharov’s Hypothesis of Cosmological Transitions with Changes in the Signature of the Metric Universe A. D. Sakharov metric signature path integral quantization unitary evolution |
| title | On A. D. Sakharov’s Hypothesis of Cosmological Transitions with Changes in the Signature of the Metric |
| title_full | On A. D. Sakharov’s Hypothesis of Cosmological Transitions with Changes in the Signature of the Metric |
| title_fullStr | On A. D. Sakharov’s Hypothesis of Cosmological Transitions with Changes in the Signature of the Metric |
| title_full_unstemmed | On A. D. Sakharov’s Hypothesis of Cosmological Transitions with Changes in the Signature of the Metric |
| title_short | On A. D. Sakharov’s Hypothesis of Cosmological Transitions with Changes in the Signature of the Metric |
| title_sort | on a d sakharov s hypothesis of cosmological transitions with changes in the signature of the metric |
| topic | A. D. Sakharov metric signature path integral quantization unitary evolution |
| url | https://www.mdpi.com/2218-1997/7/5/151 |
| work_keys_str_mv | AT tatyanapshestakova onadsakharovshypothesisofcosmologicaltransitionswithchangesinthesignatureofthemetric |