arXiv subjects
Publications and source records attributed to Phillip Josef Bachler.
We discuss various old and new definitions of the notion of a vector field on a convenient manifold that can be proved to give rise to Lie algebras, and are in finite dimensions equivalent to the standard notion of a vector field.
This paper defines coherent manifolds and discusses their properties and their application in quantum mechanics. Every coherent manifold with a large group of symmetries gives rise to a Hilbert space, the completed quantum space of $Z$, which contains a distinguished family of coherent states labeled by the points of the manifold. The second quantization map in quantum field theory is generalized to quantization operators on arbitrary coherent manifolds. It is shown how the Schrödinger equation on any such completed quantum space can be solved in terms of computations only involving the coherent product. In particular, this applies to a description of Bosonic Fock spaces as completed quantum spaces of a class of coherent manifolds called Klauder spaces.