Spacetime geometry with geometric calculus. (English) Zbl 1446.83003
Summary: Geometric Calculus is developed for curved-space treatments of General Relativity and comparison is made with the flat-space gauge theory approach by C. Doran and A. Lasenby [Geometric algebra for physicists. Cambridge: Cambridge University Press (2003; Zbl 1078.53001)] and Gull. Einstein’s Principle of Equivalence is generalized to a gauge principle that provides the foundation for a new formulation of General Relativity as a Gauge Theory of Gravity on a curved spacetime manifold. Geometric Calculus provides mathematical tools that streamline the formulation and simplify calculations. The formalism automatically includes spinors so the Dirac equation is incorporated in a geometrically natural way.
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 35Q76 | Einstein equations |
| 58A05 | Differentiable manifolds, foundations |
| 15A66 | Clifford algebras, spinors |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 83E05 | Geometrodynamics and the holographic principle |
Keywords:
principle of equivalence; gauge theory gravity; differential manifolds; Dirac equation; new formulation of General Relativity as a Gauge Theory of GravityCitations:
Zbl 1078.53001References:
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