  A central task of theoretical physics is to analyse spectral properties of
quantum mechanical observables. In this endeavour, Mourre's conjugate operator
method emerged as an effective tool in the spectral theory of Schr\"odinger
operators. This paper introduces a novel class of examples amenable to Mourre's
method, focusing on the spectra of energy-momentum operators in relativistic
quantum field theory. Under the assumption of Lorentz or dilation covariance
and the spectrum condition, we provide new proofs of the absolute continuity of
the energy-momentum spectra, showcasing the efficiency of Mourre's method in
the relativistic setting.
