  For an operator generating a group on $L^p$ spaces transference results give
bounds on the Phillips functional calculus also known as spectral multiplier
estimates. In this paper we consider specific group generators which are
abstraction of first order differential operators and prove similar spectral
multiplier estimates assuming only that the group is bounded on $L^2$ rather
than $L^p$. We also prove an R-bounded H\"ormander calculus result by assuming
an abstract Sobolev embedding property and show that the square of a perturbed
Hodge-Dirac operator has such calculus.
