Manifestly Covariant Canonical Formulation of the Yang-Mills Field Theories. I : General Formalism

概要

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A canonical formalism of the Yang-Mills theories is presented in the framework of manifestly covariant quantum field theory, which is found to give a natural extension of the Gupta-Bleuler formalism. Physical states are defined by the two subsidiary conditions Q_B|phys>=Q_c|phys>=0, where the conserved charges Q_B and Q_c are the generators of the Becchi-Rouet-Stora transformation and of the Faddeev-Popov ghost scale transformation, respectively. With the aid of the explicit expressions of Q_B and Q_c in terms of the asymptotic fields, it is proved that the physical state conditions are satisfied and, as a consequence, the physical S-matrix is unitary. It is emphasized that the Faddeev-Popov ghosts c and c^^- should be hermitian (i.e., c^<dagger>=c, c^^-=c^^-^<dagger>) in order for the Lagrangian L and the charges Q_B and Q_c to be hermitian. Only with this unconventional assignment, one can achieve a transparent and consistent formulation of the Yang-Mills theories. The structures of the total state vector space and of the physical subspace are clarified based on the detailed analysis of the asymptotic fields given in the present series of papers.
理論物理学刊行会の論文
1978-12-25