基于投影不变性的GR的扩展
Extensions of GR using Projective-Invariance
摘要：
我们表明，统一的电磁和重力到一个单一的几何实体可以漂亮地完成在一个理论与非对称仿射连接（$Γ_{μν}^λ\neqΓ_{νμ}^λ$），统一的对称性是射影对称。此外，我们表明，在一个纯粹的仿射理论中，有没有约束的对称性的$Γ_{μν}^λ$，电磁场可以被解释为保持投影不变性的领域。物质拉格朗日量打破了射影不变性，产生了经典的相对论引力和量子电磁学。我们注意到，如果把电磁场张量与第二Ricci张量联系起来，把$Γ_{[μν]}^ν$与矢势联系起来，就可以得到经典的Einstein-Maxwell方程。此外，我们解释了射影变换的几何解释。最后，我们讨论了射影不变性在f（R）引力理论中的重要作用。
英文摘要：
We show that the unification of electromagnetism and gravity into a single geometrical entity can be beautifully accomplished in a theory with non-symmetric affine connection ($Γ_{μν}^λ\neqΓ_{νμ}^λ$), and the unifying symmetry being projective symmetry. In addition, we show that in a purely-affine theory where there are no constrains on the symmetry of $Γ_{μν}^λ$, the electromagnetic field can be interpreted as the field that preserves projective-invariance. The matter Lagrangian breaks the projective-invariance, generating classical relativistic gravity and quantum electromagnetism. We notice that, if we associate the electromagnetic field tensor with the second Ricci tensor and $Γ_{[μν]}^ν$ with the vector potential, then the classical Einstein-Maxwell equation can be obtained. In addition, we explain the geometrical interpretation of projective transformations. Finally, we discuss the importance of the role of projective-invariance in f(R) gravity theories.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
