Srednicki — Quantum Field Theory · Problem 29.1

Canonical Quantization of Scalar Fields — Mark Srednicki

Physics — QFT · effective-field-theory-beta-function-universality

Problem

Consider a theory with a single dimensionless coupling

g

whose beta function takes the form

\beta(g) = b_1 g^2 + b_2 g^3 + \ldots

. Now consider a new definition of the coupling of the form

\tilde{g} = g + c_2 g^2 + \ldots

. a) Show that

\beta(\tilde{g}) = b_1\tilde{g}^2 + b_2\tilde{g}^3 + \ldots

. b) Generalize this result to the case of multiple dimensionless couplings.