TITLE:
A Contribution to the DLF-Theory: On Singularities of the SU(2,2)-Action in U(1,1)
AUTHORS:
Alexander Levichev
KEYWORDS:
Parallelizations of Space-Time Bundles, Segal’s Cosmos, Conformal Group Actions in U(2), and in U(1, 1)
JOURNAL NAME:
Journal of Modern Physics,
Vol.7 No.15,
November
4,
2016
ABSTRACT: Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is realized as the Lie group with a causal structure defined by an invariant Lorentzian form on u(1,1). Two Lie groups G, GF are introduced as representations of SU(2,2): they are related via conjugation by a certain matrix Win Gl(4). The linear-fractional action of G on D is well-known to be global, conformal, and it plays a crucial role in the analysis on space-time bundles carried out by Paneitz and Segal in the 1980’s. This analysis was based on the parallelizing group U(2). In the paper, singularities’ general (“geometric”) description of the linear-fractional conformal GF-action on F is given and specific examples are presented. The results call for the analysis of space-time bundles based on U(1,1) as the parallelizing group. Certain key stages of such an analysis are suggested.