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 samples 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.
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