  We present a novel covariant bilinear formalism for the Two Higgs Doublet
Model (2HDM) which utilises the Dirac algebra associated with the SL(2,C) group
that acts on the scalar doublet field space. This Dirac-algebra approach
enables us to obtain a fully O(1,3)-covariant and IR-safe expression for the
one-loop effective potential. We illustrate how the formalism can be used to
evaluate the breaking of global symmetries of the 2HDM potential by loop
effects, in a field-reparameterisation invariant manner.
