Prog. Theor. Phys. Vol. 59 No. 5 (1978) pp. 1699-1708

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Canonical Yang-Mills Field Theory with Invariant Gauge-Families

— Introduction of Gauge Parameters as a Group Vector —

Kan-ichi Yokoyama

Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima 725

(Received December 24, 1977)

Abstract:

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 coexists, 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 are introduced in order to guarantee the existence of a desirable physical subspace with positive semi-definite metric. As to treatment of the Faddeev-Popov ghosts, Kugo and Ojima's approach is adopted. Three supplementary conditions which are consistent with one another constrain the physical subspace.

URL : http://ptp.ipap.jp/link?PTP/59/1699/
DOI : 10.1143/PTP.59.1699

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Citing Article(s) :

Progress of Theoretical Physics Vol. 60 No. 3 (1978) pp. 927-929 :
On Finite Local Gauge Transformations in a Yang-Mills Field Theory with Invariant Gauge-Families

Kan-ichi Yokoyama, Minoru Takeda and Minoru Monda
Progress of Theoretical Physics Vol. 60 No. 4 (1978) pp. 1167-1174 :
Renormalization Scheme of a Canonical Yang-Mills Field Theory with Invariant Gauge-Families

Kan-ichi Yokoyama
Progress of Theoretical Physics Vol. 63 No. 1 (1980) pp. 275-286 :
Gauge Independence of Transition Amplitudes in Quantum Electrodynamics

Hiroaki Matsuda and Reijiro Kubo
Progress of Theoretical Physics Vol. 63 No. 4 (1980) pp. 1384-1392 :
Possible Situation for Gauge Independence of Wave-Function Renormalization Constants in Gauge-Field Theories

Takashi Fukuda, Reijiro Kubo and Kan-ichi Yokoyama
Progress of Theoretical Physics Vol. 63 No. 6 (1980) pp. 2061-2077 :
The Higgs-Kibble Model on the Basis of a Canonical Yang-Mills Field Theory with Gauge Covariance. I

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Progress of Theoretical Physics Vol. 64 No. 3 (1980) pp. 1058-1064 :
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Progress of Theoretical Physics Vol. 64 No. 4 (1980) pp. 1412-1424 :
Gauge Covariance in Non-Abelian Gauge Theories

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Progress of Theoretical Physics Vol. 67 No. 4 (1982) pp. 1206-1215 :
Quantum Theory of Massive Yang-Mills Fields. II

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Progress of Theoretical Physics Vol. 90 No. 5 (1993) pp. 1111-1120 :
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Progress of Theoretical Physics Vol. 90 No. 5 (1993) pp. 1121-1129 :
An Extension of Type I Gaugeon Formalism for Quantum Electrodynamics

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Progress of Theoretical Physics Vol. 103 No. 3 (2000) pp. 685-696 :
Gaugeon Formalism for Spin-3/2 Rarita-Schwinger Gauge Field

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Progress of Theoretical Physics Vol. 117 No. 4 (2007) pp. 695-713 :
BRST Symmetric Gaugeon Formalism for the Higgs Model

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Progress of Theoretical Physics Vol. 117 No. 4 (2007) pp. 745-763 :
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Progress of Theoretical Physics Supplement No.66 (1979) pp. 1-130 :
Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem

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