Abstract
We define a Poisson structure on the Nualart-Pardoux test algebra associated to the path space of a finite dimensional Lie algebra.
Highlights
Deformation quantization in field theory is an interesting subject [1,2,3]
We define a Poisson structure on the Nualart-Pardoux test algebra associated to the path space of a finite dimensional Lie algebra
Dito has defined the Moyal product on the algebra of Hilbert-Schmitt smooth functions on H ⊕ H∗. If they are similar to models of quantum field theory, are more tractable
Summary
Abstract: We define a Poisson structure on the Nualart-Pardoux test algebra associated to the path space of a finite dimensional Lie algebra. Has considered the canonical Poisson structure on H ⊕ H∗ where H is a Hilbert space. We would like to give an analytical meaning to the simplest Poisson structure considered in the review of Dubrovin-Novikov [12] formula (44) p 53).
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