  We consider the effects of a perpendicular magnetic field on the d-density
wave order and conclude that if the pseudogap phase in the cuprates is due to
this order, then it is highly insensitive to the magnetic field in the
underdoped regime, while its sensitivity increases as the gap vanishes in the
overdoped regime. This appears to be consistent with the available experiments
and can be tested further in neutron scattering experiments. We also
investigate the nature of the de Haas- van Alphen effect in the ordered state
and discuss the possibility of observing it.
