A geometric model for extended particles. (English) Zbl 1117.81005

Mladenov, Ivaïlo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9–14, 2006. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-37-0/pbk). 302-311 (2007).
Summary: Here we combine the ideas of a quantum functional theory intended to describe intrinsically extended particles with those of a geometrostochastic one describing stochastically extended particles. The main ingredients of the former are a physical wave \(u\) replacing the point \(x\) and a functional wave \(X[u, t]\) replacing the probability wave function of the conventional quantum theory. The latter introduces a proper wave function accounting for the unavoidable errors in the measurement of continuous observable such as the position and momentum.
For the entire collection see [Zbl 1108.53003].


81P05 General and philosophical questions in quantum theory
81V25 Other elementary particle theory in quantum theory
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory