  The broken symmetry that develops below 17.5K in the heavy fermion compound
URu2Si2 has long eluded identification. Here we argue that the recent
observation of Ising quasiparticles in URu2Si2 results from a spinor
hybridization order parameter that breaks double time-reversal symmetry by
mixing states of integer and half-integer spin. Such "hastatic order"
(hasta:[Latin]spear) hybridizes Kramers conduction electrons with Ising,
non-Kramers 5f2 states of the uranium atoms to produce Ising quasiparticles.
The development of a spinorial hybridization at 17.5K accounts for both the
large entropy of condensation and the magnetic anomaly observed in torque
magnetometry. This paper develops the theory of hastatic order in detail,
providing the mathematical development of its key concepts. Hastatic order
predicts a tiny transverse moment in the conduction sea, a collosal Ising
anisotropy in the nonlinear susceptibility anomaly and a resonant
energy-dependent nematicity in the tunneling density of states.
