Research Perspective in Stochastic Mechanics

Aubrey Truman, Ian M Davies

Steven M. Moore

Francesco Guerra

D Falco

The problem of a formulation of Nelson's (1967) stochastic mechanics of scalar fields in the context of general relativity is considered. The simple example of the scalar field in the Wightman vacuum state on the Rindler wedge is examined, the stochastic counterpart of the Fulling ambiguity of canonical quantisation is formulated, and the role of the stochastic mechanics of thermal mixtures, as formulated by Guerra and Loffredo (1981), is analysed, in the spirit of Davies (1975) and Unruh (1976), in the solution of the above ambiguity. An overall picture emerges which, both in the explicit example considered here and in its straightforward generalisations to static submanifolds of more general spacetimes, confirms Smolin's point of view that stochastic quantisation is a very natural conceptual frame in which to study the general non-covariance of the distinction between quantum and thermal fluctuations.

Khavtgain Namsrai

Philippe Blanchard, Ph. Combe, Wan Zheng