3 research outputs found
Noncommutative Unification of General Relativity and Quantum Mechanics. A Finite Model
We construct a model unifying general relativity and quantum mechanics in a
broader structure of noncommutative geometry. The geometry in question is that
of a transformation groupoid given by the action of a finite group G on a space
E. We define the algebra of smooth complex valued functions on the groupoid,
with convolution as multiplication, in terms of which the groupoid geometry is
developed. Owing to the fact that the group G is finite the model can be
computed in full details. We show that by suitable averaging of noncommutative
geometric quantities one recovers the standard space-time geometry. The quantum
sector of the model is explored in terms of the regular representation of the
groupoid algebra, and its correspondence with the standard quantum mechanics is
established.Comment: 20 LaTex pages, General Relativity and Gravitation, in pres