Algebra of Field in the Stückelberg Formalism
Minoru Omote, Yoshimasa Takaya · Progress of Theoretical Physics · 1969
Recently Lee, Weinberg and Zumino have proposed the algebra of field and derived sum rules for the spectral functions of the vector and axial vector field based on the Yang-Mills theory with mass terms. But in their formalism, the time components of the vector and axial vector fields were eliminated by using identities. Therefore from the viewpoint of relativistic invariance, their treatment is unsatisfactory. To improve this point, we employ the Stückelberg formalism for the vector fields in which the time component of vector field is treated in the same way as the other components. Therefore the relativistic covariance is clear at every step of formulation. However, we can prove the equivalence of the two theories so long as we treat the problems in the subspace of Hilbert space which satisfies the subsidiary condition.