Contractions, deformations and curvature

Details Contractions, deformations and curvature Contractions, deformations and curvature

2007-06-15

arxiv.org/abs/0706.2208v1

Int. J. Theor. Phys. 47 (2008) 649-663

Physics

Mathematical Physics

17 pages. Based on the talk given in the Oberwolfach workshop: Deformations and Contractions in Mathematics and Physics (Germa

Scientific paper

10.1007/s10773-007-9489-9

The role of curvature in relation with Lie algebra contractions of the pseudo-ortogonal algebras so(p,q) is fully described by considering some associated symmetrical homogeneous spaces of constant curvature within a Cayley-Klein framework. We show that a given Lie algebra contraction can be interpreted geometrically as the zero-curvature limit of some underlying homogeneous space with constant curvature. In particular, we study in detail the contraction process for the three classical Riemannian spaces (spherical, Euclidean, hyperbolic), three non-relativistic (Newtonian) spacetimes and three relativistic ((anti-)de Sitter and Minkowskian) spacetimes. Next, from a different perspective, we make use of quantum deformations of Lie algebras in order to construct a family of spaces of non-constant curvature that can be interpreted as deformations of the above nine spaces. In this framework, the quantum deformation parameter is identified as the parameter that controls the curvature of such "quantum" spaces.

Affiliated with

Also associated with

No associations

Rating

Contractions, deformations and curvature does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Contractions, deformations and curvature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Contractions, deformations and curvature will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-549128