Abstract
Under the assumption that the time-ordered products are given by Feynman rules with Bogoliubov's renormalization scheme, it is shown that the operator forms of Euler-Lagrange equations of motion and Noether's theorem for a wide class of perturbation Lagrangian theories for scalar fields are valid. Ward-Takahashi identities for currents in Noether's theorem are also proved without recourse to equal-time commutators, and current-algebra results follow naturally in a subclass of Lagrangian field theories. Covariant Schwinger terms are present in these identities and their nature is determined.
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