Uncertainty Relations in Deformation Quantization

Abstract

Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson, Robertson-Schrödinger and trace uncertainty relations in deformation quantization are found. Some conditions under which the uncertainty relations are minimized are also given.

28+1 pages, harvmac file, no figures, typos corrected

References in corpus (3)

• On the uncertainty relations and squeezed states for the quantum mechanics on a circle
• Negative Probability and Uncertainty Relations
• Remarks on the Extended Characteristic Uncertainty Relations

Cited by in corpus (1)

• Uncertainty relations in quantum optics. Is the photon intelligent?