Uncertainty Relations in Deformation Quantization

Details Uncertainty Relations in Deformation Quantization Uncertainty Relations in Deformation Quantization

2002-07-20

arxiv.org/abs/math/0207181v2

J.Phys.A35:10643-10662,2002

Mathematics

Quantum Algebra

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

Scientific paper

10.1088/0305-4470/35/49/312

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-Schr\"odinger and trace uncertainty relations in deformation quantization are found. Some conditions under which the uncertainty relations are minimized are also given.

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