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We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develop a stochastic Clebsch action principle, in which the noise couples to the phase space variables through a momentum map. This special coupling simplifies the structure of the resulting stochastic Hamilton equations for the momentum map. In particular, these stochastic Hamilton equations collectivize for Hamiltonians that depend only on the momentum map variable. The Stratonovich equations are derived from the Clebsch variational principle and then converted into It^o form. In comparing the Stratonovich and It^o forms of the stochastic dynamical equations governing the components of the momentum map, we find that the It^o contraction term turns out to be a double Poisson bracket. Finally, we present the stochastic Hamiltonian formulation of the collectivized momentum map dynamics and derive the corresponding Kolmogorov forward and backward equations.
This paper presents the momentum map structures which emerge in the dynamics of mixed states. Both quantum and classical mechanics are shown to possess analogous momentum map pairs. In the quantum setting, the right leg of the pair identifies the Ber
Generating functions for Clebsch-Gordan coefficients of osp(1|2) are derived. These coefficients are expressed as q goes to - 1 limits of the dual q-Hahn polynomials. The generating functions are obtained using two different approaches respectively b
In this work, we use the geometric equivalence between Fermats and Huygens principles to show that the kinematics of light propagation in a non-dispersive medium associated with a bi-metric spacetime is expressed by means of a 1-parameter family of c
The paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over L^2(R_+). Using
In this note we continue our investigations of the representation theoretic aspects of reflection positivity, also called Osterwalder--Schrader positivity. We explain how this concept relates to affine isometric actions on real Hilbert spaces and how