In a recent publication, a procedure was developed which can be used to derive completely gauge invariant models from general Lagrangian densities with N order of derivatives and M rank of tensor potential. This procedure was then used to show that unique models follow for each order, namely classical electrodynamics for N = M = 1 and linearized Gauss–Bonnet gravity for N = M = 2. In this paper, the nature of the connection between these two well-explored physical models is further investigated by means of an additional common property; a complete dual formulation. First, we give a review of Gauss–Bonnet gravity and the dual formulation of classical electrodynamics. The dual formulation of linearized Gauss–Bonnet gravity is then developed. It is shown that the dual formulation of linearized Gauss–Bonnet gravity is analogous to the homogenous half of Maxwell’s theory; both have equations of motion corresponding to the (second) Bianchi identity, built from the dual form of their respective field strength tensors. In order to have a dually symmetric counterpart analogous to the nonhomogenous half of Maxwell’s theory, the first invariant derived from the procedure in N = M = 2 can be introduced. The complete gauge invariance of a model with respect to Noether’s first theorem, and not just the equation of motion, is a necessary condition for this dual formulation. We show that this result can be generalized to the higher spin gauge theories, where the spin-n curvature tensors for all N = M = n are the field strength tensors for each n. These completely gauge invariant models correspond to the Maxwell-like higher spin gauge theories whose equations of motion have been well explored in the literature.

中文翻译：

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线性高斯-博内重力与经典电动力学之间的联系 II：完全对偶公式

在最近的出版物中，开发了一种程序，该程序可用于从一般拉格朗日密度导出完全规范不变模型ñ导数的顺序和米张量势的秩。然后使用该程序来证明每个订单都有独特的模型，即经典电动力学ñ = 米 = 1和线性化 Gauss-Bonnet 重力ñ = 米 = 2. 在本文中，这两个经过充分探索的物理模型之间的联系性质通过一个额外的共同属性进行了进一步研究；一个完整的双重公式。首先，我们回顾一下 Gauss-Bonnet 引力和经典电动力学的对偶公式。然后开发了线性高斯-博内重力的对偶公式。结果表明，线性高斯-博内引力的对偶公式类似于麦克斯韦理论的齐次半；两者都有对应于（第二个）Bianchi 恒等式的运动方程，由它们各自的场强张量的对偶形式构成。为了有一个类似于麦克斯韦理论的非齐次半的对偶对称对应物，第一个不变量来自于ñ = 米 = 2可以介绍。模型关于诺特第一定理的完全规范不变性，而不仅仅是运动方程，是这个对偶公式的必要条件。我们证明了这个结果可以推广到更高的自旋规范理论，其中自旋-n所有的曲率张量ñ = 米 = n是每个的场强张量n. 这些完全规范不变的模型对应于类似麦克斯韦的高自旋规范理论，其运动方程已在文献中得到很好的探索。