Quantum Theory of Gauge Fields with Gauge Covariance

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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.