Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-10-30
J.Math.Phys. 44 (2003) 4713-4735
Physics
High Energy Physics
High Energy Physics - Theory
section on Riemannian structure improved, references added
Scientific paper
10.1063/1.1607514
The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact connected Lie groups and G is simple. An elementary discussion of the differential geometric and bundle theoretic aspects of G/H, including its projective modules and complex, Kaehler and Riemannian structures, is presented for this purpose. An attractive feature of our approach is that it transparently shows obstructions to spin- and spin_c-structures. When a manifold is spin_c and not spin, U(1) gauge fields have to be introduced in a particular way to define spinors. Likewise, for manifolds like SU(3)/SO(3), which are not even spin_c, we show that SU(2) and higher rank gauge fields have to be introduced to define spinors. This result has potential consequences for string theories if such manifolds occur as D-branes. The spectra and eigenstates of the Dirac operator on spheres S^n=SO(n+1)/SO(n), invariant under SO(n+1), are explicitly found. Aspects of our work overlap with the earlier research of Cahen et al..
Balachandran Aiyalam P.
Immirzi Giorgio
Lee Joohan
Prešnajder Peter
No associations
LandOfFree
Dirac Operators on Coset Spaces 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 Dirac Operators on Coset Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dirac Operators on Coset Spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-578363