Abstract
A concept of quantum stochastic parallel transport is formulated in a finitely generated projective module over a “smooth” subalgebra of a C*-algebra where the noise arises from a family of semi-martingales in Fock space. The main examples studied are Heisenberg modules over the non-commutative torus where we find instances in which quantum parallel transport exists, but there is no diffusion on the underlying algebra of which it is the horizontal lift.
Work carried out while the author was supported by SERC Grant No GR/D51292.
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© 1988 Springer-Verlag
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Applebaum, D. (1988). Quantum stochastic parallel transport on non-commutative vector bundles. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications III. Lecture Notes in Mathematics, vol 1303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078052
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DOI: https://doi.org/10.1007/BFb0078052
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