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arXiv 0712.3532hep-th
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具有紧致额外维的量子场论的新调节子。一：基本原理

New Regulators for Quantum Field Theories with Compactified Extra Dimensions. I: Fundamentals

Sky Bauman, Keith R. Dienes

备注：
47 pages, LaTeX, 3 figures
发表信息：
Phys.Rev.D77:125005,2008
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摘要：

在本文中，我们提出了两个新的调节器的量子场论在紧致额外维时空。我们将这些调节器称为“扩展硬截止”（EHC）和“扩展维正则化”（EDR）。虽然基于传统的四维调节器，但这些高维调节器的关键新特征是，它们是专门设计来处理混合时空的，其中一些维度是无限大的，而另一些维度是紧化的。此外，与其他大多数在额外维度文献中使用的调节器不同，这些调节器被设计为尊重在紧化之前存在的原始高维洛伦兹和规范对称性，而不仅仅是之后保留的四维对称性。这种区别对于计算激发的卡鲁扎-克莱因模本身的物理学特别重要，而不仅仅是它们对零模的辐射效应。通过尊重完整的高维对称性，我们的调节器避免了引入伪项，这些伪项不容易从紧化的物理效应中解脱出来。作为我们工作的一部分，我们还得到了一些辅助结果。例如，我们证明，在规范不变的理论，类似的沃德-高桥恒等式不仅适用于通常的零模（四维）光子，但所有激发卡鲁扎-克莱因光子以及。

英文摘要：

In this paper, we propose two new regulators for quantum field theories in spacetimes with compactified extra dimensions. We refer to these regulators as the ``extended hard cutoff'' (EHC) and ``extended dimensional regularization'' (EDR). Although based on traditional four-dimensional regulators, the key new feature of these higher-dimensional regulators is that they are specifically designed to handle mixed spacetimes in which some dimensions are infinitely large and others are compactified. Moreover, unlike most other regulators which have been used in the extra-dimension literature, these regulators are designed to respect the original higher-dimensional Lorentz and gauge symmetries that exist prior to compactification, and not merely the four-dimensional symmetries which remain afterward. This distinction is particularly relevant for calculations of the physics of the excited Kaluza-Klein modes themselves, and not merely their radiative effects on zero modes. By respecting the full higher-dimensional symmetries, our regulators avoid the introduction of spurious terms which would not have been easy to disentangle from the physical effects of compactification. As part of our work, we also derive a number of ancillary results. For example, we demonstrate that in a gauge-invariant theory, analogues of the Ward-Takahashi identity hold not only for the usual zero-mode (four-dimensional) photons, but for all excited Kaluza-Klein photons as well.

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