  The validity of the ergodic hypothesis in quantum systems can be rephrased in
the form of the eigenstate thermalisation hypothesis (ETH), a set of
statistical properties for the matrix elements of local observables in energy
eigenstates, which is expected to hold in any ergodic system. We test the ETH
in a nonintegrable model of relativistic quantum field theory (QFT) using the
numerical method of Hamiltonian truncation in combination with analytical
arguments based on Lorentz symmetry and renormalisation group theory. We find
that there is an infinite sequence of eigenstates with the characteristics of
quantum many-body scars, that is, exceptional eigenstates with observable
expectation values that lie far from thermal values, and we show that these
states are one-quasiparticle states. We argue that in the thermodynamic limit
the eigenstates cover the entire area between two diverging lines: the line of
one-quasiparticle states, whose direction is dictated by relativistic
kinematics, and the thermal average line. Our results suggest that the strong
version of the ETH is violated in any relativistic QFT whose spectrum admits a
quasiparticle description.
