Non-Riemannian Geometry of Continuous-Spin Infinite- Particle Systems and Their Non-Interaction Representation
We give a formulation of continuous-spin (taking values in a smooth compact n-manifold, the one-particle space) infinite particle systems with interactions described by a Gibbsian potential, in terms of stochastic differential geometry. We give invariant constructions for the interaction representation of the random dynamics. In the case of n ≠ 1 (thus excluding the XY-model) we construct a pure-noise representation equivalent to the interaction representation, by constructing the LeJan-Watanabe representation for the Riemann-Cartan- Weyl linear connection defined by the Gibbsian measure and the metric on the single-particle manifold.
KeywordsCauchy Problem Gibbs Measure Interaction Representation Linear Connection Block Operator
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