规范自由与相对论：电磁学、引力和狄拉克场的统一处理
Gauge Freedom and Relativity: A Unified Treatment of Electromagnetism, Gravity and the Dirac Field
摘要：
广义相对论的几何性质被重新考虑为一个特定的非线性相互作用的领域在一个平坦的背景下，感知的几何形状和坐标是“物理”实体，是由一个非直观的关系，以底层领域的可观察机构拼凑内插。物理学中这种更普遍的规范概念为把所有领域置于类似的地位打开了一扇重要的大门，但需要仔细重新考虑物理学中的张量以及围绕它们的传统智慧。讨论了平坦背景和诱导守恒量的含义，并与诱导物理坐标下的“可观测”正定能量和概率密度进行了对比。在这种背景下，狄拉克矩阵被提升为动态原引力场和“物理度量”信息的保持者。波函数的独立姐妹场在这些场中被用于双线性而不是二次拉格朗日。这种构造极大地扩大了规范群，因此现在证明场的规范不变函数的因果演化相对于物理度规而言，需要应力能量守恒和概率流守恒定律。通过类希格斯耦合项，原引力场产生了一个定义良好的物理度规结构，并在相对于类希格斯耦合的低能量下给出了引力与电磁的通常区别。平坦的背景诱导了一整套守恒定律，但结果需要将这些量与由记录设备和观测器从场中观察到的量区分开来。
英文摘要：
The geometric properties of General Relativity are reconsidered as a particular nonlinear interaction of fields on a flat background where the perceived geometry and coordinates are "physical" entities that are interpolated by a patchwork of observable bodies with a nonintuitive relationship to the underlying fields. This more general notion of gauge in physics opens an important door to put all fields on a similar standing but requires a careful reconsideration of tensors in physics and the conventional wisdom surrounding them. The meaning of the flat background and the induced conserved quantities are discussed and contrasted with the "observable" positive definite energy and probability density in terms of the induced physical coordinates. In this context, the Dirac matrices are promoted to dynamic proto-gravity fields and the keeper of "physical metric" information. Independent sister fields to the wavefunctions are utilized in a bilinear rather than a quadratic lagrangian in these fields. This construction greatly enlarges the gauge group so that now proving causal evolution, relative to the physical metric, for the gauge invariant functions of the fields requires both the stress-energy conservation and probability current conservation laws. Through a Higgs-like coupling term the proto-gravity fields generate a well defined physical metric structure and gives the usual distinguishing of gravity from electromagnetism at low energies relative to the Higgs-like coupling. The flat background induces a full set of conservation laws but results in the need to distinguish these quantities from those observed by recording devices and observers constructed from the fields.
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