格点上全同玻色子系综的泛函积分和随机表示
Functional Integral and Stochastic Representations for Ensembles of Identical Bosons on a Lattice
摘要：
正则相干态泛函积分推导出在晶格上的相同玻色子的合奏，正则化是一个离散化的欧几里德时间。收敛的时间-连续极限示出了各种离散行动。重点是正则系综中的配分函数和期望值的积分表示。连接到巨正则积分，和一些差异，进行了讨论。证明了协方差的一致界，简化了时间-连续极限的分析，也可用于热力学极限的分析。相互作用的随机游动的合奏的随机表示的关系是明确的，并讨论了其修改存在的凝聚。
英文摘要：
Regularized coherent-state functional integrals are derived for ensembles of identical bosons on a lattice, the regularization being a discretization of Euclidian time. Convergence of the time-continuum limit is shown for various discretized actions. The focus is on the integral representation for the partition function and expectation values in the canonical ensemble. The connection to the grand-canonical integral, and a number of differences, are discussed. Uniform bounds for covariances are proven, which simplify the analysis of the time-continuum limit and can also be used to analyze the thermodynamic limit. The relation to a stochastic representation by an ensemble of interacting random walks is made explicit, and its modifications in presence of a condensate are discussed.
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