Quantum and classical conserved quantities: Martingales, conservation laws and constants of motion
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 (Refereed)
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.
, Abel Symposia, 2
IdentifiersURN: urn:nbn:se:kth:diva-40725ISI: 000248622000020ScopusID: 2-s2.0-84883629975ISBN: 978-3-540-70846-9OAI: oai:DiVA.org:kth-40725DiVA: diva2:442982
2nd Abel Symposium held in Honor of Kiyosi Ito Location: Oslo, Norway, Date: JUL 29-AUG 04, 2005