dc.contributor.advisor | Hervik, Sigbjørn | |
dc.contributor.advisor | Kruglikov, Boris | |
dc.contributor.author | Helleland, Christer | |
dc.date.accessioned | 2020-08-26T10:37:06Z | |
dc.date.available | 2020-08-26T10:37:06Z | |
dc.date.issued | 2020-09 | |
dc.identifier.citation | A mathematical approach to Wick rotations by Christer Helleland. Stavanger : University of Stavanger, 2020 (PhD thesis UiS, no. 536) | en_US |
dc.identifier.isbn | 978-82-7644-943-3 | |
dc.identifier.issn | 1890-1387 | |
dc.identifier.uri | https://hdl.handle.net/11250/2674362 | |
dc.description.abstract | In this thesis we define Wick-rotations mathematically using pseudo-Riemannian geometry, and relate Wick-rotations to real geometric invariant theory (GIT). We discover some new results concerning the existence of Wick rotations (of various signatures). For instance we show that a Wick-rotation of a pseudo-Riemannian space (at a fixed point p) to a Riemannian space forces the space to be Riemann purely electric (RPE). We also define compatibility among representations and relate them to real GIT and Wick-rotations. The polynomial curvature invariants of pseudo-Riemannian spaces are also considered and related to Wick-rotations.
Wick-rotations of a special class of pseudo-Riemannian manifolds (M; g) are also studied; namely Lie groups G equipped with left-invariant metrics. We prove some new results concerning the existence of real slices (of Lie algebras) of certain signatures of a holomorphic inner product space (gC; gC) (on a complex Lie algebra). The definition of a Cartan involution for a semisimple Lie algebra is defined for a general Lie algebra equipped with a pseudo-inner product: (g; g), and the theorems of Cartan (concerning Cartan involutions) are generalised and proved. For instance we prove that a pseudo-Riemannian Lie group (G; g) can be Wick-rotated to a Riemannian Lie group ( ~ G; ~g) if and only if there exist a Cartan involution of the Lie algebra g. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Stavanger: Universitetet i Stavanger | en_US |
dc.relation.ispartofseries | PhD thesis UiS;536 | |
dc.relation.haspart | Paper 1: Helleland, C., Hervik, S. (2018) Wick-rotations and real GIT. Journal of Geometry and Physics, 123, pp. 343-361. https://doi.org/10.1016/j.geomphys.2017.09.009 | en_US |
dc.relation.haspart | Paper 2: Helleland, C., Hervik, S. (2018) Wick-rotatable metric is purely electric. Journal of Geometry and Physics, 123, pp. 424-429. https://doi.org/10.1016/j.geomphys.2017.09.015 | en_US |
dc.relation.haspart | Paper 3: Helleland, C., Hervik, S. (2019) Real GIT with applications to compatible representations and Wick-rotations. Journal of Geometry and Physics, 142, pp. 92-110. https://doi.org/10.1016/j.geomphys.2019.03.007 | en_US |
dc.relation.haspart | Paper 4: Wick-rotations of pseudo-Riemannian Lie groups. Submitted to Journal of Geometry and Physics. | en_US |
dc.subject | fysikk | en_US |
dc.subject | Wick-rotasjoner | en_US |
dc.subject | matematisk fysikk | en_US |
dc.title | A mathematical approach to Wick rotations | en_US |
dc.type | Doctoral thesis | en_US |
dc.rights.holder | © 2019 Christer Helleland | en_US |
dc.subject.nsi | VDP::Matematikk og Naturvitenskap: 400::Fysikk: 430 | en_US |