Collective modes in the d-density wave state of the cuprates

Using a functional integral formulation, we analyze the collective modes in the $d$-density wave state. Since only discrete symmetries are broken, no massless phase mode is present. The only relevant fluctuation is the amplitude fluctuation of the order parameter, which is treated at the gaussian level above the long range order. These fluctuations give rise to a massive mode, the analog of the U(1) Higgs, or amplitude mode at wave-vector $(\pi ,\pi )$. Neutrons in inelastic neutron scattering experiments couple to this mode via the orbital currents and are likely to produce direct measurements of this amplitude boson.