Towards the Unification of Gravity and other Interactions: What has been Missed?

Abstract

Faced with the persisting problem of the unification of gravity with other fundamental interactions we investigate the possibility of a new paradigm, according to which the basic space of physics is a multidimensional space $\mathcal{C}$ associated with matter configurations. We consider general relativity in $\mathcal{C}$. In spacetime, which is a 4-dimensional subspace of $\mathcal{C}$, we have not only the 4-dimensional gravity, but also other interactions, just as in Kaluza-Klein theories. We then consider a finite dimensional description of extended objects in terms of the center of mass, area, and volume degrees of freedom, which altogether form a 16-dimensional manifold whose tangent space at any point is Clifford algebra Cl(1,3). The latter algebra is very promising for the unification, and it provides description of fermions.

11 pages; Talk presented at "First Mediterranean Conference on Classical and Quantum Gravity", Kolymbari, Crete, Greece, 14-18 September 2009

References in corpus (5)

• Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime
• Kaluza-Klein Theory without Extra Dimensions: Curved Clifford Space
• Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings
• Classical dynamics on triangleland
• On a Unified Theory of Generalized Branes Coupled to Gauge Fields, Including the Gravitational and Kalb-Ramond Fields