论文标题
$ f \ left（b^2 \右）$修改Weyl重力
Spinor field solutions in $F\left(B^2\right)$ modified Weyl gravity
论文作者
论文摘要
我们考虑经过修饰的Weyl重力，其中狄拉克纺纱球场与重力无限耦合。假定这种修饰的重力是描述与重力旋转场有关的量子引力效应的一些近似值。结果表明，这种理论包含一类指标的解决方案，这些指标在HOPF纤维上等同于HOPF指标。在这种情况下，我们获得了解决方案的完整离散范围，并表明它们与HOPF纤维上的HOPF不变。获得了HOPF坐标中自旋算子的表达式。已经证明，这类在共同等效的指标中包含：（a）描述没有异国物质的环形虫洞的度量； （b）带有弹跳和通货膨胀的宇宙学解决方案； （c）随着度量签名变化的过渡。对结果进行了物理讨论。 \ end {摘要}
We consider modified Weyl gravity where a Dirac spinor field is nonminimally coupled to gravity. It is assumed that such modified gravity is some approximation for the description of quantum gravitational effects related to the gravitating spinor field. It is shown that such a theory contains solutions for a class of metrics which are conformally equivalent to the Hopf metric on the Hopf fibration. For this case, we obtain a full discrete spectrum of the solutions and show that they can be related to the Hopf invariant on the Hopf fibration. The expression for the spin operator in the Hopf coordinates is obtained. It is demonstrated that this class of conformally equivalent metrics contains: (a) a metric describing a toroidal wormhole without exotic matter; (b) a cosmological solution with a bounce and inflation; and (c) a transition with a change in metric signature. A physical discussion of the results is given. \end{abstract}
