  We prove the local wellposedness of the Cauchy problems for the electron
magnetohydrodynamics equations (E-MHD) without resistivity for possibly large
perturbations of nonzero uniform magnetic fields. While the local wellposedness
problem for (E-MHD) has been extensively studied in the presence of resistivity
(which provides dissipative effects), this seems to be the first such result
without resistivity. (E-MHD) is a fluid description of plasma in small scales
where the motion of electrons relative to ions is significant. Mathematically,
it is a quasilinear dispersive equation with nondegenerate but nonelliptic
second-order principal term. Our result significantly improves upon the
straightforward adaptation of the classical work of Kenig--Ponce--Rolvung--Vega
on the quasilinear ultrahyperbolic Schr\"odinger equations, as the regularity
and decay assumptions on the initial data are greatly weakened to the level
analogous to the recent work of Marzuola--Metcalfe--Tataru in the case of
elliptic principal term.
  A key ingredient of our proof is a simple observation about the relationship
between the size of a symbol and the operator norm of its quantization as a
pseudodifferential operator when restricted to high frequencies. This allows us
to localize the (non-classical) pseudodifferential renormalization operator
considered by Kenig--Ponce--Rolvung--Vega, and produce instead a classical
pseudodifferential renormalization operator. We furthermore incorporate the
function space framework of Marzuola--Metcalfe--Tataru to the present case of
nonelliptic principal term.
