Canonical Yang-Mills Field Theory with Invariant Gauge-Families : Introduction of Gauge Parameters as a Group Vector

概要

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A canonical Yang-Mills field theory with indefinite metric is presented on the basis of a covariant gauge formalism for quantum electrodynamics. As the first step of the formulation, a many-gauge field problem, in which many massless Abelian-gauge fields coexist, is treated from a new standpoint. It is shown that only a single pair of a gaugeon field and its associated one can govern the gauge structure of the whole system. The result obtained is further extended to cases of non-Abelian gauge theories. Gauge parameters for respective components of the Yang-Mills fields are introduced as a group vector. There exists a q-number local gauge transformation which connects relevant fields belonging to the same invariant gauge family with one another in a manifestly covariant way. In canonical quantization, the Faddeev-Popov ghosts, Kugo and Ojima's approach is adopted. Three supplementary conditions which are consistent with one another constrain the physical subspace.
理論物理学刊行会の論文
1978-05-25