论文标题
评论定义实时路径在晶格理论中不可或缺的集成的微妙之处
Comment on the subtlety of defining real-time path integral in lattice gauge theories
论文作者
论文摘要
最近，Hoshina，Fujii和Kikukukawa指出，Minkowski签名中的幼稚晶格仪理论的动作并未导致连续限制的单一理论，Kanwar和Wagman提出了对Wilson Action而没有分歧的替代晶格行动。我们在这里表明，可以从修改后的贝塞尔函数的渐近扩展中理解微妙之处，该函数已讨论了非质量量子力学中紧凑型变量的路径积分的讨论。定义适当的连续理论的基本要素是$ i \ varepsilon $处方，并且通过正确实现$ i \ varepsilon $，我们表明Wilson Action可以用于实时路径积分。在这里，重要的是，应为Qimelike和Spacelike Plaquettes实施$ i \ varepsilon $。我们还争辩说，汉密尔顿形式主义的威尔逊行动所必需的$ i \ varepsilon $的原因。需要$ i \ varepsilon $来表现出奇异路径的贡献，为此，威尔逊动作可以从实际的连续性动作中给出不同的价值。
Recently, Hoshina, Fujii, and Kikukawa pointed out that the naive lattice gauge theory action in Minkowski signature does not result in a unitary theory in the continuum limit, and Kanwar and Wagman proposed alternative lattice actions to the Wilson action without divergences. We here show that the subtlety can be understood from the asymptotic expansion of the modified Bessel function, which has been discussed for path integral of compact variables in nonrelativistic quantum mechanics. The essential ingredient for defining the appropriate continuum theory is the $i\varepsilon$ prescription, and with the proper implementation of the $i\varepsilon$ we show that the Wilson action can be used for the real-time path integrals. It is here important that the $i\varepsilon$ should be implemented for both timelike and spacelike plaquettes. We also argue the reason why the $i\varepsilon$ becomes required for the Wilson action from the Hamiltonian formalism. The $i\varepsilon$ is needed to manifestly suppress the contributions from singular paths, for which the Wilson action can give different values from those of the actual continuum action.
