The quantization of actual platforms relocating on staff and symmetric areas has been a space of lively study during the last 3 a long time. This publication indicates that it truly is attainable to introduce a illustration self reliant propagator for a true, separable, hooked up and easily hooked up Lie team with irreducible, square-integrable representations. For a given set of kinematical variables this propagator is a unmarried generalized functionality self reliant of any specific number of fiducial vector and the irreducible representations of the Lie team generated by way of those kinematical variables,which still properly propagates every one component to the continual illustration in line with the coherent states linked to those kinematical variables. moreover, the booklet indicates that it's attainable to build regularized lattice part direction integrals for a true, separable, attached and easily attached Lie staff with irreducible, square-integrable representations, and even if the configuration house is generally a multidimensional curved manifold, it's proven that the ensuing lattice section house course indispensable has the shape of a lattice part area course fundamental on a multidimensional flat manifold. accordingly, a singular and very average section area direction quintessential quantization is got for normal actual platforms whose kinematical variables are the turbines of a hooked up and easily attached Lie staff. This novel section area course essential quantization is (a) precise, (b) extra normal than, and (c) loose from the constraints of the formerly thought of direction indispensable quantization of loose actual platforms relocating on workforce manifolds.
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