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Quantum and classical conserved quantities: Martingales, conservation laws and constants of motion
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2007 (English)In: Stochastic Analysis and Applications / [ed] Benth, FE; DiNunno, G; Lindstrom, T; Oksendal, B; Zhang, T, 2007, Vol. 2, 461-491 p.Conference paper, Published paper (Refereed)
Abstract [en]

We study a class of diffusions, conjugate Brownian motion, related to Brownian motion in Riemannian manifolds. Mappings that, up to a change of time scale, carry these processes into each other, are characterised. The characterisation involves conformality and a space-time version of harmonicity. Infinitesimal descriptions are given and used to produce martingales and conservation laws. The relation to classical constants of motion is presented, as well as the relation to Noether's theorem in classical mechanics and field theory.

Place, publisher, year, edition, pages
2007. Vol. 2, 461-491 p.
Series
Abel Symposia, 2
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-40725ISI: 000248622000020Scopus ID: 2-s2.0-84883629975ISBN: 978-3-540-70846-9 (print)OAI: oai:DiVA.org:kth-40725DiVA: diva2:442982
Conference
2nd Abel Symposium held in Honor of Kiyosi Ito Location: Oslo, Norway, Date: JUL 29-AUG 04, 2005
Available from: 2011-09-23 Created: 2011-09-20 Last updated: 2011-09-23Bibliographically approved

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