1978/12/01 by Taichiro Kugo, Izumi Ojima · 5 citations
Physics and Astronomy · Computer Science · #Cold Atom Physics and Bose-Einstein Condensates #Quantum chaos and dynamical systems #Quantum Information and Cryptography #Covariant transformation #Physics #Mathematical physics #Hermitian matrix #Formalism (music) #Canonical transformation #Quantum field theory #Theoretical physics #Quantum mechanics #Classical mechanics #Quantum
paper · pdf · doi:10.1143/ptp.60.1869
openalex publication_date 1978/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22
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 QB|phys〉= QC|phys〉 = 0, where the conserved charges QB and QC 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 QB and QC 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 ̄sc should be hermitian (i.e., c† = c, ̄sc = ̄sc>†) in order for the Lagrangian L and the charges QB and QC 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.