Differential Operators on Smooth Manifolds

Abstract

The property of a differential operator on a smooth manifold M to be invariant with respect to an action of some group G (especially a Lie group) on M plays a great role in mathematical physics since it helps select physically significant operators. The algebra Diff_G(M) of all G-invariant differential operators with complex or real coefficients on M gives the material for constructing G-invariant physical theories on M. Properties of such theory are in close connection with properties of the algebra Diff_G(M).