By using the spacetime algebra, we explain the helical motion of the electron (zitterbewegung) and its Coulomb field by introducing a mechanism that breaks locally the electromagnetic gauge invariance. We show that this gauge invariance is broken in all points of spacetime, except for those that correspond to that cylindrical helix which is the electron's world line, and that it gives rise to an oscillating Coulomb-like field with frequency equal to the zitterbewegung one. This field is found to satisfy the so-called Maxwell-London equations. This oscillating field, when averaged over a zitterbewegung period, is the usual Coulomb field of the electron.31941699203208