Canonical Quantization of Non-Abelian Gauge Fields

概要

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A canonical quantization is applied in an unambiguous way to a non-abelian gauge field under a condition of the Coulomb gauge. The ambiguity with respect to the order of quantized field variables is avoided by performing a transition from the classical to the quantum theory before removing the constraint imposed on the state vectors. The constraint which causes a big trouble with the violation of the unitarity of the S-matrix is transformed into a simple one which shows that the physical state vectors should be functionals of the transversal field variables. The Hamiltonian derived after this transformation becomes a complicated functional of the transversal fields. The S-matrix is easily derived from this Hamiltonian by following the conventional procedure. The well-known trouble due to the time derivatives of field variables in the decomposition of T-products in the S-matrix is overcome by introducing a strange singular term to the Hamiltonian which is identical with the DeWitt term in the Coulomb gauge. A brief discussion is made on the relationship between our result and those already published in other papers.
理論物理学刊行会の論文
1976-05-25