  The principle of minimal coupling has been used in the study of Higgs boson
interactions to argue that certain higher dimensional operators in the
low-energy effective theory generalization of the Standard Model are suppressed
by loop factors, and thus smaller than others. It also has been extensively
used to analyze beyond-the-standard-model theories. We show that in field
theory, and even in quantum mechanics, the concept of minimal coupling is
ill-defined and inapplicable as a general principle, and give many pedagogical
examples which illustrate this fact. We also clarify some related
misconceptions about the dynamics of strongly coupled gauge theories. Many
arguments in the literature on Higgs boson interactions that use minimal
coupling, particularly in pseudo-Goldstone Higgs theories, are inherently
flawed.
