Figueroa-O'Farrill, José

Lucietti, James

Grassie, Ross

Engineering and Physical Sciences Research Council (EPSRC)

2021-11-12T10:48:34Z

2021-11-12T10:48:34Z

2021-11-27

This thesis presents a framework in which to explore kinematical symmetries beyond the standard Lorentzian case. This framework consists of an algebraic classification, a geometric classification, and a derivation of the geometric properties required to define physical theories on the classified spacetime geometries. The work completed in substantiating this framework for kinematical, super-kinematical, and super-Bargmann symmetries constitutes the body of this thesis. To this end, the classification of kinematical Lie algebras in spatial dimension D = 3, as presented in [3,4], is reviewed; as is the classification of spatially-isotropic homogeneous spacetimes of [5]. The derivation of geometric properties such as the non-compactness of boosts, soldering forms and vielbeins, and the space of invariant affine connections is then presented. We move on to classify the N = 1 kinematical Lie superalgebras in three spatial dimensions, finding 43 isomorphism classes of Lie superalgebras. Once these algebras are determined, we classify the corresponding simply-connected homogeneous (4|4)-dimensional superspaces and show how the resulting 27 homogeneous superspaces may be related to one another via geometric limits. Finally, we turn our attention to generalised Bargmann superalgebras. In the present work, these will be the N = 1 and N = 2 super-extensions of the Bargmann and Newton-Hooke algebras, as well as the centrally-extended static kinematical Lie algebra, of which the former three all arise as deformations. Focussing solely on three spatial dimensions, we find 9 isomorphism classes in the N = 1 case, and we identify 22 branches of superalgebras in the N = 2 case.

https://hdl.handle.net/1842/38261

http://dx.doi.org/10.7488/era/1527

en

The University of Edinburgh

J. Figueroa-O’Farrill, R. Grassie, and S. Prohazka, “Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes,” arXiv:1905.00034 [hep-th].

J. Figueroa-O’Farrill and R. Grassie, “Kinematical superspaces,” arXiv:1908.11278 [hep-th].

symmetry classification

Lorentzian symmetry

kinematical symmetry

super-Bargmann symmetry

kinematical Lie algebras

Beyond Lorentzian symmetry

Thesis or Dissertation

Doctoral

PhD Doctor of Philosophy