Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-03-08
Commun.Math.Phys. 182 (1996) 155-176
Physics
High Energy Physics
High Energy Physics - Theory
30 pages, Plain TeX
Scientific paper
10.1007/BF02506388
We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element $ds$. Its unitary representations correspond to Riemannian metrics and Spin structure while $ds$ is the Dirac propagator $ds = \ts \!\!$---$\!\! \ts = D^{-1}$ where $D$ is the Dirac operator. We extend these simple relations to the non commutative case using Tomita's involution $J$. We then write a spectral action, the trace of a function of the length element in Planck units, which when applied to the non commutative geometry of the Standard Model will be shown (in a joint work with Ali Chamseddine) to give the SM Lagrangian coupled to gravity. The internal fluctuations of the non commutative geometry are trivial in the commutative case but yield the full bosonic sector of SM with all correct quantum numbers in the slightly non commutative case. The group of local gauge transformations appears spontaneously as a normal subgroup of the diffeomorphism group.
No associations
LandOfFree
Gravity coupled with matter and foundation of non-commutative geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Gravity coupled with matter and foundation of non-commutative geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gravity coupled with matter and foundation of non-commutative geometry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-234796