Feynman-Kac semigroups, ground state diffusions, and large deviations
Feynman-Kac semigroups, ground state diffusions, and large deviations
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Feynman-Kac 半群、基态扩散和大偏差
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发表时间：
1994
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通讯作者：
Liming Wu
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作者：
Liming Wu
本文研究了广义Schrodinger算子−L + V，其中L是L2（E，m）上对称马氏半群（Pt）的生成元，以及相应的Dirichlet形式EV。利用Cramer泛函Λ（V）给出了EV是下有界的充要条件和Feynman-Kac半群（PVt）是有界的充要条件.也给出了−L + V的本质自伴性的一些充分条件。通过大偏差，我们找到了一个新的条件，保证了−L + V的基态φ的存在，我们构造了基态过程Qφt，其生成元在扩散情形下由Lφ = L + φ−1Γ（φ，·）给出，其中Γ是与L相关的方场算符。讨论了Lφ的自伴性。作为应用，我们考虑了抽象Wiener空间上二次量子化半群的扰动，欧氏量子场的时间演化，以及随机量子化。
We study the generalized Schrodinger operator −L + V, where L is the generator of a symmetric Markov semigroup (Pt) on L2(E, m), and the corresponding Dirichlet form EV. By means of the Cramer functional Λ(V), we give necessary and sufficient conditions for EV to be lower bounded and for the Feynman-Kac semigroup (PVt) to be bounded. Some sufficient conditions for the essential self-adjointness of −L + V are also given. By means of large deviations, we find a new condition which ensures the existence of ground state φ of −L + V and we construct the ground state process Qφt, whose generator is given in the diffusion case by Lφ = L + φ−1Γ(φ, · ), where Γ is the square field operator associated to L. The self-adjointness of Lφ is discussed. As applications, we consider perturbation of the semigroups of second quantization on an abstract Wiener space, the time evolution of euclidean quantum fields, and stochastic quantization.