We elevate the field theoretical similarities between Maxwell and Weyl vector fields into a full local scale/gauge invariant Weyl/Maxwell mutual sourcing theory. In its preliminary form, and exclusively in four dimensions, the associated Lagrangian is dynamical scalar field free, hosts no fermion matter fields, and Holdom kinetic mixing is switched off. The mutual sourcing term is then necessarily spacetime curvature (not just metric) dependent, and inevitably Ricci linear, suggesting that a non-vanishing spacetime curvature can in principle induce an electromagnetic current. In its mature form, however, the Weyl/Maxwell mutual sourcing idea serendipitously constitutes a novel variant of the gravitational Weyl-Dirac (incorporating Brans-Dicke) theory. Counter intuitively, and again exclusively in four dimensions, the optional quartic scalar potential gets consistently replaced by a Higgs-like potential, such that the co-divergence of the Maxwell vector field resembles a conformal vacuum expectation value.

中文翻译：

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Ricci线性Weyl / Maxwell相互采购

我们将麦克斯韦场与Weyl向量场之间的场理论相似性提升为完整的局部尺度/尺度不变的Weyl / Maxwell互源理论。在其初步形式中，并且仅在四个维度上，关联的拉格朗日算子没有动力学标量场，没有费米子物质场，并且Holdom动力学混合已关闭。因此，互源项必定依赖于时空曲率（而不仅仅是度量），并且不可避免地是Ricci线性的，这表明不消失的时空曲率原则上可以感应电磁电流。然而，在其成熟的形式中，Weyl / Maxwell相互采购的思想偶然地构成了引力Weyl-Dirac（包含Brans-Dicke）理论的一种新颖变体。直观地进行反算，并再次在四个维度上反算，