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arXiv · math-ph/0209016

Product structure of heat phase space and branching Brownian motion

Frederic P. Schuller·Pascal Vogt
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Abstract

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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Frederic P. Schuller, Pascal Vogt. 2003-06-23. Product structure of heat phase space and branching Brownian motion. https://doi.org/10.1016/s0003-4916(03)00172-6

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