Conformal motions and the Duistermaat-Heckman integration formula
نویسندگان
چکیده
منابع مشابه
Conformal Motions and the Duistermaat-Heckman Integration Formula
We derive a geometric integration formula for the partition function of a classical dynamical system and use it to show that corrections to the WKB approximation vanish for any Hamiltonian which generates conformal motions of some Riemannian geometry on the phase space. This generalizes previous cases where the Hamiltonian was taken as an isometry generator. We show that this conformal symmetry...
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Here we develop an explicitly covariant expression for the stationary phase approximation of a classical partition function based on geometric properties of the phase space. As an example of the utility of such an evaluation we show that in the case of the Hamiltonian ows generating conformal rescalings of the underlying geometry, the classical partition function is given exactly by the leading...
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Lutian Zhao UID: 661622198 The Duistermaat-Heckman theorems concern the measure associated to moment map of a torus action of symplectic manifold. Typically, this name refers to two theorems, one is called the ”Duistermaat-Heckman measure", which says that ”the Radon-Nikodym derivative is piecewise polynomial", the definition of each terms will be introduced later. The second one is called ”Dui...
متن کاملThe Log-concavity Conjecture for the Duistermaat-heckman Measure Revisited
Karshon constructed the first counterexample to the log-concavity conjecture for the Duistermaat-Heckman measure: a Hamiltonian six manifold whose fixed points set is the disjoint union of two copies of T. In this article, for any closed symplectic four manifold N with b > 1, we show that there is a Hamiltonian circle manifold M fibred over N such that its DuistermaatHeckman function is not log...
متن کاملExample of a Non-log-concave Duistermaat-heckman Measure
We construct a compact symplectic manifold with a Hamiltonian circle action for which the Duistermaat-Heckman function is not log-concave.
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ژورنال
عنوان ژورنال: Physics Letters B
سال: 1996
ISSN: 0370-2693
DOI: 10.1016/0370-2693(96)00086-x