Dirac charge quantization and generalized differential cohomology

Quantization of Higher Abelian Gauge Theory in Generalized Differential Cohomology

We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger–Simons cohomology, and of Ramond–Ramond fields in Type II superstring theory and differential K-theory.

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

Dirac Cohomology for the Cubic Dirac Operator

Let g be a complex semisimple Lie algebra and let r ⊂ g be any reductive Lie subalgebra such that B|r is nonsingular where B is the Killing form of g. Let Z(r) and Z(g) be, respectively, the centers of the enveloping algebras of r and g. Using a Harish-Chandra isomorphism one has a homomorphism η : Z(g) → Z(r) which, by a well-known result of H. Cartan, yields the the relative Lie algebra cohom...

Quantization of Dirac Field

Induction Functor in Non-commutative Equivariant Cohomology and Dirac Cohomology

The aim of this paper is to put some recent results of HuangPandz̆ić (conjectured by Vogan) and Kostant on Dirac cohomology in a broader perspective. This is achieved by introducing an induction functor in the noncommutative equivariant cohomology. In this context, the results of Huang-Pandz̆ić and Kostant are interpreted as special cases (corresponding to the manifold being a point) of more gene...