Immobile Excitations and Alternative Arithmetic

I will give a derivation of some properties of "fracton phases" with the help of "finite fields."

In ordinary matter, without disorder, the behavior is as if there were quantized excitations moving freely through the system, because momentum is conserved.    In fracton phases,  single-particle excitations cannot move. For example, the energy dispersion is perfectly flat and degenerate.  The phenomenon was discovered by Jeongwan Haah; he came up with them as a way to make stable quantum q-bits. 

I will give an explanation for why fractons cannot move by finding plane-wave conservation laws based, not on complex numbers, but on a sort of modular arithmetic Fourier analysis, which is also used in error correcting codes.