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。规范形式主义提供了一个更广泛的框架，实现量子水平上的规范协变性。迄今为止，这种形式主义已知适用于电动力学和杨-米尔斯理论。本研究的目的是将该理论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（对应于量子规范自由）的理论中，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。这个空间可以被看作是同构于标准的久吾-大岛形式主义的希尔伯特空间，具有任意值的规范固定参数。(b)我们引入了反对称张量规范场的规范场。我们应该小心对待这类场，因为FP鬼场和规范场本身也是规范场。在秩为2的反对称张量规范场的情况下，规范场变成了矢量规范场，它与朗道规范中的张量规范场相似。对矢量规范场进行了BRST量子化，阐明了矢量规范场FP鬼场和规范场的性质。(c)超引力场中的引力子可以看作是自旋为3/2的拉里塔-施温格规范场。我们给出了自旋为3/2的规范场的规范形式，并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.