Abstract
Galilean gauge theories are quantized according to Dirac's theory of canonical quantization of constrained systems. Only the zero-momentum term in the Fourier expansion of the gauge fields is compatible with the constraints, and it is different from zero for periodic boundary conditions, while it is zero if the fields are required to vanish on the surface of the quantization box. Such a term has physical effects which therefore depend on boundary conditions. The effect of the zero-momentum term of the electric potential is to forbid charged states. This constraint holds both in the Abelian and non-Abelian case and it is true also in the relativistic theory. The zero-momentum term of the magnetic potential in the Abelian case gives rise to only radiative corrections (which are the $c\ensuremath{\rightarrow}\ensuremath{\infty}$ limit of the relativistic ones), while in the non-Abelian case it also affects the matter-field interaction.
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