2 + 1维空间中具有自对偶非度量向量的薛定谔联络
Schrödinger connection with selfdual nonmetricity vector in 2+1 dimensions
摘要：
我们提出了一个三维度规仿射引力理论，其场方程导致了几十年前薛定谔引入的连接。薛定谔联系虽然涉及非度量性，但在平行输运下保持了向量的长度，因此似乎比外尔提出的联系更物理。通过考虑常数标量曲率的解决方案，我们得到了一个自对偶关系的非度量向量，这意味着一个Proca方程，也可以解释在非齐次麦克斯韦方程组出现仿射几何。
英文摘要：
We present a three-dimensional metric affine theory of gravity whose field equations lead to a connection introduced by Schrödinger many decades ago. Although involving nonmetricity, the Schrödinger connection preserves the length of vectors under parallel transport, and appears thus to be more physical than the one proposed by Weyl. By considering solutions with constant scalar curvature, we obtain a self-duality relation for the nonmetricity vector which implies a Proca equation that may also be interpreted in terms of inhomogeneous Maxwell equations emerging from affine geometry.
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