Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$ Λ -Kantowski–Sachs universe
Abstract The system under study is the $$\Lambda $$ Λ -Kantowski–Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dic...
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oai:doaj.org-article:a45e14ed53fa4ad2b2819b7052e8c79c2021-12-05T12:09:12ZTime-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$ Λ -Kantowski–Sachs universe10.1140/epjc/s10052-021-09866-31434-60441434-6052https://doaj.org/article/a45e14ed53fa4ad2b2819b7052e8c79c2021-12-01T00:00:00Zhttps://doi.org/10.1140/epjc/s10052-021-09866-3https://doaj.org/toc/1434-6044https://doaj.org/toc/1434-6052Abstract The system under study is the $$\Lambda $$ Λ -Kantowski–Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations $$t=f({\tilde{t}})$$ t = f ( t ~ ) ) decay probability is defined and thus “observers” which correspond to different gauge choices obtain, by default, the same results. The time of decay for a Gaussian wave packet localized around the point $$a=0$$ a = 0 (where a the radial scale factor) is calculated to be of the order $$\sim 10^{-42}{-}10^{-41}~\text {s}$$ ∼ 10 - 42 - 10 - 41 s . The acquired value is near the end of the Planck era (when comparing to a FLRW universe), during which the quantum effects are most prominent. Some of the results are compared to those obtained by following the well known canonical quantization of cosmological systems, i.e. the solutions of the Wheeler–DeWitt equation.Theodoros PailasNikolaos DimakisPetros A. TerzisTheodosios ChristodoulakisSpringerOpenarticleAstrophysicsQB460-466Nuclear and particle physics. Atomic energy. RadioactivityQC770-798ENEuropean Physical Journal C: Particles and Fields, Vol 81, Iss 12, Pp 1-16 (2021) |
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Astrophysics QB460-466 Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 |
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Astrophysics QB460-466 Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Theodoros Pailas Nikolaos Dimakis Petros A. Terzis Theodosios Christodoulakis Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$ Λ -Kantowski–Sachs universe |
| description |
Abstract The system under study is the $$\Lambda $$ Λ -Kantowski–Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations $$t=f({\tilde{t}})$$ t = f ( t ~ ) ) decay probability is defined and thus “observers” which correspond to different gauge choices obtain, by default, the same results. The time of decay for a Gaussian wave packet localized around the point $$a=0$$ a = 0 (where a the radial scale factor) is calculated to be of the order $$\sim 10^{-42}{-}10^{-41}~\text {s}$$ ∼ 10 - 42 - 10 - 41 s . The acquired value is near the end of the Planck era (when comparing to a FLRW universe), during which the quantum effects are most prominent. Some of the results are compared to those obtained by following the well known canonical quantization of cosmological systems, i.e. the solutions of the Wheeler–DeWitt equation. |
| format |
article |
| author |
Theodoros Pailas Nikolaos Dimakis Petros A. Terzis Theodosios Christodoulakis |
| author_facet |
Theodoros Pailas Nikolaos Dimakis Petros A. Terzis Theodosios Christodoulakis |
| author_sort |
Theodoros Pailas |
| title |
Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$ Λ -Kantowski–Sachs universe |
| title_short |
Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$ Λ -Kantowski–Sachs universe |
| title_full |
Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$ Λ -Kantowski–Sachs universe |
| title_fullStr |
Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$ Λ -Kantowski–Sachs universe |
| title_full_unstemmed |
Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$ Λ -Kantowski–Sachs universe |
| title_sort |
time-covariant schrödinger equation and invariant decay probability: the $$\lambda $$ λ -kantowski–sachs universe |
| publisher |
SpringerOpen |
| publishDate |
2021 |
| url |
https://doaj.org/article/a45e14ed53fa4ad2b2819b7052e8c79c |
| work_keys_str_mv |
AT theodorospailas timecovariantschrodingerequationandinvariantdecayprobabilitythelambdalkantowskisachsuniverse AT nikolaosdimakis timecovariantschrodingerequationandinvariantdecayprobabilitythelambdalkantowskisachsuniverse AT petrosaterzis timecovariantschrodingerequationandinvariantdecayprobabilitythelambdalkantowskisachsuniverse AT theodosioschristodoulakis timecovariantschrodingerequationandinvariantdecayprobabilitythelambdalkantowskisachsuniverse |
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1718372210720112640 |