An outlook on quantum gravity from an algebraic perspective

Details An outlook on quantum gravity from an algebraic perspective An outlook on quantum gravity from an algebraic perspective

2010-03-23

arxiv.org/abs/1003.4434v1

Physics

Mathematical Physics

39 pages, 1 xy-pic figure, LaTex

Scientific paper

The first part is a review of a cross-section of the literature on algebraic methods in non-perturbative quantum gravity focusing on viewing algebra as a laboratory in which to deepen understanding of the nature of geometry. In the second part we describe a new algebraic characterisation of the Dirac operator in noncommutative geometry and then use it to make predictions about the form of the fermion mass matrix. Assimilating and building on the various ideas described in the review, the final part consists of an outline of a new perspective on (noncommutative) quantum spectral gravity. This is the second of a pair of papers on this subject.

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