一维空间中大质量实标量场时空传播子的精确结果、瞬态广义吉布斯系综与解析近似
Exact results, transient generalized Gibbs ensembles, and analytic approximations for spacetime propagators of massive, real scalar fields in one spatial dimension
AI总结：
本文全面研究一维大质量实标量场传播子，重新推导精确结果，引入瞬态广义吉布斯系综理解，并给出仅含初等函数的解析近似。
摘要：
由一维空间中的克莱因-戈尔登方程描述的大质量实标量场是玻色子量子场论中最基本的例子。几十年来，它一直被研究，或作为一个简单的学术理论，或作为低维系统中现实的新兴多体理论。尽管如此，其传播子的时空行为很少成为焦点，尽管已知精确结果，但在描述上仍存在空白，且缺乏深入物理解析。本文旨在通过提供结果的全面讨论来解决这些不足，并表明这一旧理论仍能产生若干新结果和洞见。首先，我们通过提供完整的重新推导来回顾已知结果，并补充讨论空间和时间变量如何精确地扩展到复值以确保整个时空的解析性。这一过程还展示了光锥上的奇点如何被正则化以与解析性和质量消失的物理极限保持兼容。通过考虑场与非相对论热库的接触，提供了向非零温度的扩展，这对于凝聚态系统中新兴场理论是必要的。随后，表明瞬态、短时空传播可以在现代发展的广义吉布斯系综背景下理解，该系综描述了一个无质量理论，其有效温度由克莱因-戈尔登质量和物理温度设定。最后，提出了一个近似方案，该方案捕捉了传播子在整个时空中非平凡的质量依赖性，但仅涉及初等函数。
英文摘要：
The massive, real scalar field described by the Klein-Gordon equation in one spatial dimension is the most elementary example of a bosonic quantum field theory. It has been investigated for many decades either as a simple academic theory or as a realistic emergent many-body theory in low-dimensional systems. Despite this, the space and time behavior of its propagators have rarely been in the foreground, and although exact results are known, there remain gaps in the description and a lack of an in-depth physical analysis. The aim of this paper is to address the deficits by providing a comprehensive discussion of the results, and to show that this old theory still allows for several new results and insights. To start, we review the known results by providing a rederivation in full detail, to which we add a discussion on how exactly space and time variables need to be extended to complex values to ensure analyticity throughout spacetime. This procedure shows also how singularities on the lightcone need to be regularized to remain compatible with the analyticity and the physical limit of a vanishing mass. An extension to nonzero temperatures is provided by considering the contact of the field to a nonrelativistic thermal reservoir, such as is necessary for emerging field theories in condensed matter systems. Subsequently, it is shown that the transient, short spacetime propagation can be understood in the context of the modern development of a generalized Gibbs ensemble, which describes a massless theory with an effective temperature that is set by the Klein-Gordon mass and the physical temperature. Finally, an approximation scheme is presented that captures the non-trivial mass dependence of the propagators throughout all spacetime but involves only elementary functions.
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