从统一的2 T-场论看含自旋的1 T-场论的对偶性
Dualities among 1T-Field Theories with Spin, Emerging from a Unifying 2T-Field Theory
摘要：
两次物理学（2 T-物理学）和普通的一次物理学公式（1 T-物理学）之间的关系类似于一个在房间里移动的三维物体和它从不同角度投射在墙上的多个阴影之间的关系。卡在墙上的观察者看到的多重阴影类似于普通1 T时空中经历的2 T宇宙的效应。在本文中，我们开发了一些定量方面的场论的背景下，这种2 T到1 T的关系。本文讨论了d+2维的2 T场论及其在包含Klein-Gordon场、Dirac场和Yang-Mills场（如粒子和力的标准模型）的1 T场论形式下的影子。我们证明了影子1 T场论之间必然存在隐藏的联系。这些关系表现为对偶性和隐藏的时空对称性。阴影的一个子集是不同引力背景（不同时空）中的1 T场论，如平坦的闵可夫斯基时空、罗伯逊-沃克膨胀宇宙、AdS（d-k）x S（k）和其他，包括奇异的。我们明确地构造了这个共形平坦子集之间的对偶变换，并构造了它们的隐SO（d，2）对称性的生成元。1 T场论之间存在这种隐藏的关系，可以通过1 T物理学的理论和实验来检验，这是d+2维时空和统一的2 T物理结构的基础证据的一部分。
英文摘要：
The relation between two time physics (2T-physics) and the ordinary one time formulation of physics (1T-physics) is similar to the relation between a 3-dimensional object moving in a room and its multiple shadows moving on walls when projected from different perspectives. The multiple shadows as seen by observers stuck on the wall are analogous to the effects of the 2T-universe as experienced in ordinary 1T spacetime. In this paper we develop some of the quantitative aspects of this 2T to 1T relationship in the context of field theory. We discuss 2T field theory in d+2 dimensions and its shadows in the form of 1T field theories when the theory contains Klein-Gordon, Dirac and Yang-Mills fields, such as the Standard Model of particles and forces. We show that the shadow 1T field theories must have hidden relations among themselves. These relations take the form of dualities and hidden spacetime symmetries. A subset of the shadows are 1T field theories in different gravitational backgrounds (different space-times) such as the flat Minkowski spacetime, the Robertson-Walker expanding universe, AdS(d-k) x S(k) and others, including singular ones. We explicitly construct the duality transformations among this conformally flat subset, and build the generators of their hidden SO(d,2) symmetry. The existence of such hidden relations among 1T field theories, which can be tested by both theory and experiment in 1T-physics, is part of the evidence for the underlying d+2 dimensional spacetime and the unifying 2T-physics structure.
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