Non-Commutative Geometry on Quantum Phase-Space

@misc{citeulike:894228, abstract = {A non--commutative analogue of the classical differential forms is constructed on the phase--space of an arbitrary quantum system. The non--commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. <br />They are constructed by applying the Weyl--Wigner symbol map to the differential envelope of the linear operators on the quantum mechanical Hilbert space. This leads to a representation of the non--commutative forms considered by A.\~{}Connes in terms of multiscalar functions on the classical phase--space. In an appropriate coincidence limit they define a quantum deformation of the classical tensor fields and both commutative and non--commutative forms can be studied in a unified framework. We interprete the quantum differential forms in physical terms and comment on possible applications.}, author = {Reuter, M. }, citeulike-article-id = {894228}, eprint = {hep-th/9510011}, keywords = {noncommutative, quantum-phase-space}, month = {Oct}, posted-at = {2006-10-12 14:03:23}, priority = {2}, title = {Non-Commutative Geometry on Quantum Phase-Space}, url = {http://arxiv.org/abs/hep-th/9510011}, year = {1995} }

TY - ELEC ID - citeulike:894228 L3 - citeulike-article-id:894228 TI - Non-Commutative Geometry on Quantum Phase-Space N2 - A non--commutative analogue of the classical differential forms is constructed on the phase--space of an arbitrary quantum system. The non--commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. <br />They are constructed by applying the Weyl--Wigner symbol map to the differential envelope of the linear operators on the quantum mechanical Hilbert space. This leads to a representation of the non--commutative forms considered by A.~Connes in terms of multiscalar functions on the classical phase--space. In an appropriate coincidence limit they define a quantum deformation of the classical tensor fields and both commutative and non--commutative forms can be studied in a unified framework. We interprete the quantum differential forms in physical terms and comment on possible applications. KW - noncommutative KW - quantum-phase-space AU - Reuter, M PY - 1995/Oct/04/ UR - http://arxiv.org/abs/hep-th/9510011 ER -