CONSTRUCTION OF COVARIANT AND GAUGE INVARIANT T' PRODUCTS

The problem of constructing sea-gull terms, which render time-ordered products of arbitrary operators Lorentz covariant, is investigated. We determine the necessary and sufficient conditions that the commutators of operators must satisfy in order that it be possible to covariantize their time-ordered product. We give an explicit formula for the sea-gull in terms of the relevant Schwinger term. We show that our considerations, which use formal equal time commutators, are equally valid for commutators defined by use of the Bjorken-Johnson-Low theorem. We then address ourselves to the question of whether sea-gulls and Schwinger terms cancel in the Ward-Takahashi identities which these covariant T* products satisfy. We give necessary and sufficient conditions for this cancellation to take place. Specific examples of the general theory are given. © 1969.