An Extra Structure of Spacetime: A Space of Points, Areas and Volumes
arXiv:gr-qc/0611050 · doi:10.1088/1742-6596/66/1/012022
Abstract
A theory in which points, lines, areas and volumes are on on the same footing is investigated. All those geometric objects form a 16-dimensional manifold, called C-space, which generalizes spacetime. In such higher dimensional space fundamental interactions can be unified \` a la Kaluza-Klein. The ordinary, 4-dimensional, gravity and gauge fields are incorporated in the metric and spin connection, whilst the conserved gauge charges are related to the isometries of curved C-space. It is shown that a conserved generator of an isometry in C-space contains a part with derivatives, which generalizes orbital angular momentum, and a part with the generators of Clifford algebra, which generalizes spin.
arXiv comment13 pages; A talk presented at the XXIX Spanish Relativity Meeting ERE 2006, 4th-8th September 2006, Palma de Mallorca, Spain
References in corpus (13)
- Spin Foam Models for Quantum Gravity
- Physical States in Matter-Coupled Dilaton Gravity
- Functional Schroedinger and BRST Quantization of (1+1)--Dimensional Gravity
- Kaluza-Klein Theory without Extra Dimensions: Curved Clifford Space
- Higher Derivative Gravity and Torsion from the Geometry of C-spaces
- Clifford Space as the Arena for Physics
- Quenched, Minisuperspace, Bosonic p-brane Propagator
- Fuzzy dimensions and Planck's Uncertainty Principle for p-branes
- Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings
- Pseudo Euclidean-Signature Harmonic Oscillator, Quantum Field Theory and Vanishing Cosmological Constant
- Dimensionally Democratic Calculus and Principles of Polydimensional Physics
- Generalization of the Coleman-Mandula Theorem to Higher Dimension
- Clifford Space as a Generalization of Spacetime: Prospects for Unification in Physics