Dimensional regularization

Summary

Dimensional regularization makes divergent Feynman diagram integrals finite by computing them in a spacetime of dimension $d$, treated as a complex variable. The integrals become meromorphic functions of $d$, and the divergences of four-dimensional integrals reappear as poles at $d = 4$. It preserves Lorentz invariance and gauge invariance, which is why it is the standard tool for the renormalization of gauge theories.