Abstract
The Yang‐Mills gradient flow and its extension to the fermion field provide a very general method to obtain renormalized observables in gauge theory. The method is applicable also with nonperturbative regularization such as lattice. The gradeint flow thus offers useful probes to study non-perturbative dynamics of gauge theory. In this work, aiming at possible simplification in perturbative calculations associated with the gradient flow, a modification of the gauge-fixed version of the flow equation, which preserves gauge covariance under the background gauge transformation, is proposed. This formulation allows for example a very quick one-loop calculation of the small flow time expansion of a composite operator that is rele vant to the construction of a lattice energy‐momentum tensor. Some details of the calculation, which have not been given elsewhere, are presented.
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