4-vector potential transformation under gauge fixing involves changing the 4-vector potential without altering the electric (E) and magnetic (B) fields. This is achieved by modifying the 3-vector part of the potential, as changes that add a 3-vector with zero curl do not affect the B field. Gauge fixing simplifies calculations by imposing specific conditions on the 4-vector potential, allowing for easier problem-solving. Common gauge fixing conditions exist to streamline these calculations while maintaining the gauge-invariant nature of the equations. Ultimately, this ensures that results remain consistent across different gauge choices, provided no errors occur.