Functional Differential Calculus of Operators

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Abstract
The functional derivative with respect to operators of operator functionals is defined for operators which satisfy certain commutation relations of interest in quantum field theory. From this definition, a functional differential calculus is developed for functionals of tensor as well as spinor fields. It is noted that an implicit definition of the functional derivative can always be given while an explicit one seems to exist only for those operator fields which need not be restricted by supplementary operator conditions, and for which not more than one derivative occurs in the commutation relations.

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