$PT$对称性、共形对称性和电磁学的度规
$PT$ Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism
摘要：
我们提出了$PT$对称性和共形对称性之间的一些有趣的联系。我们用它们来发展电磁学的度量理论，其中电磁场存在于几何联系中。然而，与第一个提出这种可能性的Weyl不同，我们不认为连接是真实的，而是$PT$对称的，它是$iA_μ$，而不是$A_μ$本身，然后出现在连接中。通过这种修正，得到了电磁与费米子的标准最小耦合。通过使用扭转，我们得到了一个度量的电磁理论，它对称地对待它的电和磁部门，与共形不变的引力理论被发现出现。一个扩展到非阿贝尔的情况下提供。
英文摘要：
We present some interesting connections between $PT$ symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be $PT$ symmetric, with it being $iA_μ$ rather than $A_μ$ itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided.
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。
