Graded differential equations and Dirac type operators (Q1304733)

Fundamental ideas of geometric asymptotics of linear differential operators are described in terms of graded category within the framework of the jet theory of sections of vector bundles. In more detail, the author recalls the category of graded and filtered vector spaces and algebras, linear differential operators on vector bundles including prolongations and symbols, the filtrations associated with wave-like solutions \((\hbar\)-adic filtrations) and the corresponding characteristic submanifolds and transfer operators. Then the results are applied to the Dirac operator where the transfer describing the propagation of singularities yields an invariant definition of the Pauli operator.