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首页> 外文期刊>Infinite dimensional analysis, quantum probability, and related topics >SCHRODINGER OPERATORS ON LOCAL FIELDS: SELF-ADJOINTNESS AND PATH INTEGRAL REPRESENTATIONS FOR PROPAGATORS
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SCHRODINGER OPERATORS ON LOCAL FIELDS: SELF-ADJOINTNESS AND PATH INTEGRAL REPRESENTATIONS FOR PROPAGATORS

机译：局部场上的Schrodinger算子：传播子的自结合和路径积分表示

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摘要

We consider quantum systems that have as their configuration spaces finite-dimensional vector spaces over local fields. The quantum Hilbert space is taken to be a space with complex coefficients and we include in our model particles with internal symmetry. The Hamiltonian operator is a pseudo-differential operator that is initially only formally defined. For a wide class of potentials we prove that this Hamiltonian is well-defined as an unbounded self-adjoint operator. The free part of the operator gives rise to a measure on the Skorokhod space of paths, D[0, infinity), and with respect to this measure there is a path integral representation for the semigroup associated to the Hamiltonian. We prove this Feynman-Kac formula in the local field setting as a consequence of the Hille-Yosida theory of semigroups.
机译：我们考虑在局部场上具有有限维矢量空间作为其配置空间的量子系统。量子希尔伯特空间被视为具有复杂系数的空间，我们在模型中包括具有内部对称性的粒子。哈密​​顿算子是一个伪微分算子，最初只是正式定义。对于广泛的潜力，我们证明该哈密顿量被定义为无界的自伴算子。算符的自由部分在路径的Skorokhod空间上产生一个测度D [0，无穷大]，并且相对于该测度，存在与哈密顿量相关的半群的路径积分表示。由于Hille-Yosida半群理论的结果，我们在局部场环境中证明了该Feynman-Kac公式。

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