  We present a lensless, Fourier-transform ghost imaging scheme by exploring
the fourth-order correlation function of spatially incoherent thermal neutron
waves. This technique is established on the Fermi-Dirac statistics and the
anti-bunching effect of fermionic fields, and the analysis must be fully
quantum mechanical. The spinor representation of neutron waves and the
derivation purely from the Schrodinger equation makes our work the first,
rigorous, robust and truly fermionic ghost imaging scheme. The investigation
demonstrates that the coincidence of the intensity fluctuations between the
reference arm and the sample arm is directly related to the lateral
Fourier-transform of the longitudinal projection of the sample's atomic and
magnetic spatial distribution. By avoiding lens systems in neutron optics, our
method can potentially achieve de Broglie wavelength level resolution,
incomparable by current neutron imaging techniques. Its novel capability to
image crystallined and noncrystallined samples, especially the micro magnetic
structures, will bring important applications to various scientific frontiers.
