Proceedings of the International Conference on Geometry, Integrability and Quantization

Geometric Flow Appearing in Conservation Law in Classical and Quantum Mechanics

Naohisa Ogawa

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Abstract

The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional curved surface with thickness $\epsilon$ embedded in $\mathbb E^3$. In such a system, two-dimensional conservation law needs an additional term just like an anomaly. The additional term can be obtained by the $\epsilon$ expansion. This term has a Gaussian and a mean curvature dependence and can be written as the total divergence of geometric flow $J^i_{G}$. This fact holds in both classical and quantum mechanics.

Article information

Source
Proceedings of the Twentieth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Vladimir Pulov and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2019), 215-226

Dates
First available in Project Euclid: 21 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1545361495

Digital Object Identifier
doi:10.7546/giq-20-2019-215-226

Mathematical Reviews number (MathSciNet)
MR3887752

Zentralblatt MATH identifier
07060440

Citation

Ogawa, Naohisa. Geometric Flow Appearing in Conservation Law in Classical and Quantum Mechanics. Proceedings of the Twentieth International Conference on Geometry, Integrability and Quantization, 215--226, Avangard Prima, Sofia, Bulgaria, 2019. doi:10.7546/giq-20-2019-215-226. https://projecteuclid.org/euclid.pgiq/1545361495


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