论文标题
Fermionic理论的框架协变形式主义
Frame Covariant Formalism for Fermionic Theories
论文作者
论文摘要
我们为量子场理论提出了一种框架和重新对准不变的形式主义，其中包括费米子的自由度。我们使用田间空间协方差的方法和Vilkovisky-Dewitt（VDW）有效动作实现了这一目标。我们明确构建了一个场空间的超曼群，量子场在上面充当坐标。我们展示了如何从在现场重新构度下协变的经典动作中定义该超曼佛的场空间张量。然后，我们采用这些张量为田间空间的超曼佛配备度量，从而解决了关于费米文理论的正确定义的长期存在的问题。通过如此定义的度量，我们使用良好的田间空间技术来扩展VDW的有效作用，并以框架和野外反射性不变的方式表达任何费米论理论。
We present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky-DeWitt (VDW) effective action. We explicitly construct a field-space supermanifold on which the quantum fields act as coordinates. We show how to define field-space tensors on this supermanifold from the classical action that are covariant under field reparametrisations. We then employ these tensors to equip the field-space supermanifold with a metric, thus solving a long-standing problem concerning the proper definition of a metric for fermionic theories. With the metric thus defined, we use well-established field-space techniques to extend the VDW effective action and express any fermionic theory in a frame- and field-reparametrisation-invariant manner.
