International Journal of Theoretical Physics

, Volume 47, Issue 2, pp 534–552 | Cite as

Homotopy Approach to Quantum Gravity

  • David Ritz Finkelstein


Gravity may be a quantum-space-time effect. General relativity is quantized by small generic changes in its commutation relations that make its Lie algebras simple on all levels, positing extra variables frozen by self-organization as needed. This quantizes space-time coordinates as well as fields and eliminates physical singularities. Fermi statistics and sl (nℝ) Lie algebras are assumed for all levels. Spin 1/2 is taken to be anomalous, arising from vacuum organization; the spin-statistics relation is incorporated. The gravitational field is quartic in Fermi variables. Einstein’s non-commutativity of parallel transport emerges as a vestige of Heisenberg’s quantum non-commutativity near the classical limit.


Clifford Algebra Casimir Operator Singular Limit Fermi Statistic Killing Form 
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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.School of PhysicsGeorgia Institute of TechnologyAtlantaUSA

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