 Dimensional regularization

Dimensional regularization analytically continues loop integrals from an integer spacetime dimension to $d=d_0-ϵ$. Ultraviolet logarithms then appear as poles in $1/ϵ$.

Dimensional regularization is a mathematical technique used in quantum field theory to handle ultraviolet divergences (infinities) that arise in loop integrals during the calculation of Feynman diagrams. The method involves extending the number of spacetime dimensions from the usual integer values (like 4 in our physical universe) to a complex or arbitrary value, typically denoted as \(d\).