Quantum Theory of Gauge Fields with Gauge Covariance

在量子化规范理论的标准形式中，我们不能考虑量子规范自由度。规范形式提供了一个在量子水平上实现规范协方差的更广泛的框架。到目前为止，这种形式主义已知适用于电动力学和杨-米尔斯理论。本研究的目的是将形式主义应用于其他类型的规范场，并阐明该理论的量子规范结构。(A)在规范场具有BRST对称性的理论中(对应于量子规范自由度)，我们可以定义在量子规范变换下不变的物理希尔伯特空间。可以看出，这个空间与具有任意值规范固定参数的标准Kugo-Ojima形式的Hilbert空间同构。(B)我们引入了反对称张量规范场的规范场。我们应该谨慎对待这类场，因为FP鬼场和规范场本身也是规范场。在秩2反对称张量规范场的情况下，规范场变成一个矢量规范场，它与朗道规范中的张量规范场解耦。我们对矢量规范场进行了BRST量子化，阐明了矢量规范场的FP重影和规范子的性质。(C)超引力中的引力子可以看作是自旋为3/2的Rarita-Schwinger规范场。给出了自旋3/2规范场的规范形式，定义了该理论的规范不变物理希尔伯特空间。

In the standard formalism of quantized gauge theories, we cannot consider the quantum gauge freedom. The gaugeon formalism provides a wider framework which realize the gauge covariance on the quantum level. This formalism is known so far applicable to the electrodynamics and the Yang-Mills theory. The aim of the present research is to apply the formalism to other types of gauge fields and to clarify the quantum gauge structure of the theory. We have the following results :(a) In the theory with BRST symmetry for the gaugeon fields (corresponding to the quantum gauge freedom), we can define the physical Hilbert space which is invariant under the quantum gauge transformation. This space can be seen to be isomorphic to the Hilbert space of the standard Kugo-Ojima formalism with an arbitrary valued gauge fixing parameter.(b) We have introduced gaugeon fields for the anti-symmetric tensor gauge fields. We should be careful to treat this kind of fields since FP ghost fields and gaugeon fields themselves are also gauge fields. In the case of rank-2 anti-symmetric tensor gauge field, the gaugeon fields becomes a vector gauge field, which decouples to the tensor gauge fields in the Landau gauge. We have carried out the BRST quantization of the vector gaugeon field, and clarified the properties of the FP ghosts and gaugeons for the vector gaugeon field.(c) The gravitino in the supergravity can be considered as a spin-3/2 Rarita-Schwinger gauge field. We have provided the gaugeon formalism for the spin-3/2 gauge field and defined the gauge invariant physical Hilbert space of the theory.