Three-loop renormalization of the effective potential

Renormalization of the effective potential is investigated using the Coleman-Weinberg method of summing up Feynman graphs. We promote this pure graphical method to the position of Jackiw's thorough algebraic proof of his loop expansion prescription for the effective potential. The three-loop effective potential of massive phi(4) theory is calculated. We also point out that in the literature there is a misconception in renormalizing the effective potential, which is not revealed in the low(er)-level calculation. Pie support our assertion by checking a stringent requirement that dangerous pole terms be canceled among each other. [S0556-2821(97)07722-9].