SYMMETRY REDUCTION OF BROWNIAN MOTION AND QUANTUM CALOGERO–MOSER MODELS
Keyword(s):
Let Q be a Riemannian G-manifold. This paper is concerned with the symmetry reduction of Brownian motion in Q and ramifications thereof in a Hamiltonian context. Specializing to the case of polar actions, we discuss various versions of the stochastic Hamilton–Jacobi equation associated to the symmetry reduction of Brownian motion and observe some similarities to the Schrödinger equation of the quantum–free particle reduction as described by Feher and Pusztai [10]. As an application we use this reduction scheme to derive examples of quantum Calogero–Moser systems from a stochastic setting.
2002 ◽
Vol 43
(11)
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pp. 5183-5222
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Keyword(s):
2021 ◽
2010 ◽
Vol 32
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pp. 63-87
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2002 ◽
Vol 43
(11)
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pp. 5223-5253
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2014 ◽
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pp. 1450066
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2001 ◽
Vol 16
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pp. 5061-5084
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