General Ward-Like Relations in Canonical Field Theory
Yasushi Takahashi, Takao Goto · Progress of Theoretical Physics · 1977
Infinitesimal canonical transformation of a field operator is written in terms of the chronological product of the field operator and the generating current. This relation is then generalized to the infinitesimal transformation of the chronological (and retarded) products of any number of field operators. It is shown that the general relations thus obtained contain identities known as the generalized Ward relations in various forms. The general relations given in integral form are converted into differential form. The relation to the similar identities obtained by the path integral method is discussed and use of the general relations is suggested. The argument of a previous paper is, thus, refined and extended in three aspects: (i) constraint variables are treated systematically, (ii) it is pointed out that the general relations hold true for the retarded products, (iii) relation to the path integral method is discussed.