Product structure of heat phase space and branching Brownian motion

Details Product structure of heat phase space and branching Brownian motion Product structure of heat phase space and branching Brownian motion

2002-09-09

arxiv.org/abs/math-ph/0209016v2

Annals Phys. 308 (2003) 528-554

Physics

Mathematical Physics

32 pages, journal version. Annals of Physics, N.Y. (to appear)

Scientific paper

10.1016/S0003-4916(03)00172-6

A generical formalism for the discussion of Brownian processes with non-constant particle number is developed, based on the observation that the phase space of heat possesses a product structure that can be encoded in a commutative unit ring. A single Brownian particle is discussed in a Hilbert module theory, with the underlying ring structure seen to be intimately linked to the non-differentiability of Brownian paths. Multi-particle systems with interactions are explicitly constructed using a Fock space approach. The resulting ring-valued quantum field theory is applied to binary branching Brownian motion, whose Dyson-Schwinger equations can be exactly solved. The presented formalism permits the application of the full machinery of quantum field theory to Brownian processes.

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