Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator [x,p]=if(p). We apply this deformed quantization to free scalar field theory for f±= 1±βp2. The resulting quantum field theories have a rich fine scale structure. For small wavelength modes, the Green's function for f+ exhibits a remarkable transition from Lorentz to Galilean invariance, whereas for f- such modes effectively do not propagate. For both cases Lorentz invariance is recovered at long wavelengths. © 2013 American Physical Society.