Investigations have revealed a very complex structure for the coefficient functions accompanying the divergences for individual time(x+)-ordered diagrams in light-front perturbation theory. No guidelines seem to be available to look for possible mistakes in the structure of these coefficient functions emerging at the end of a long and tedious calculation, in contrast to covariant field theory. Since, in light-front field theory, the transverse boost generator is a kinematical operator which acts just like the two-dimensional Galilean boost generator in nonrelativistic dynamics, it may provide some constraint on the resulting structures. In this work we investigate the utility of Galilean symmetry beyond tree level in the context of coupling constant renormalization in light-front QCD using the two-component formalism. We show that for each x+-ordered diagram separately, the underlying transverse boost symmetry fixes relative signs of terms in the coefficient functions accompanying the diverging logarithms. We also summarize the results leading to coupling constant renormalization for the most general kinematics.
Second central extension in Galilean covariant field theory