Functional Differential Calculus of Operators. II

The calculus of operators developed in a previous paper is here carried through in momentum space. The differential quotient, i.e., the derivative of an operator with respect to a free-field operator is expressed algebraically by means of generalized functions and certain commutators. No recourse is made to configuration space but the resultant calculus in p-space is related to the previously developed one in x-space by means of Fourier transforms. The calculus is presented for spins 0, ½, and 1. The difficulties which were encountered before in the calculus for charged vector fields are resolved by working with a field equation which incorporates the supplementary condition needed to eliminate the spin-zero components.