Four-phase power from one-phase?
There is no such thing as "regular wall-socket power." That is typically 120 V, 60 Hz or 240 V, 50 Hz or something close to that depending on where you live. Capacitors might be ok, but any change in the magnetic circuit will have an effect. Another option is change the AC to DC then use complex switching circuits to simulate multi-phase AC. Most such requirements are too complex to recommend an approach with a simple answer.