Christof Wetterich derived a new exact evolution equation for the scale dependence of an effective action, which is particularly useful for dealing with infrared problems in theories with massless modes in dimensions less than four. The equation for the effective potential allows for a useful truncation, making it applicable to high-temperature phase transitions in particle physics and critical exponent calculations in statistical mechanics. The evolution equation is expressed in terms of the exact propagator, which is the second functional derivative of the effective action. The equation is derived by adding a piece to the kinetic term and including sources, leading to a $k$-dependent generating functional. The evolution equation is shown to reduce to the one-loop equation under a suitable truncation, and it provides a systematic way to compute corrections to the one-loop results. The scale $k$ acts as an infrared cutoff, ensuring that large momentum contributions are exponentially suppressed. The author also discusses the conditions under which the equation holds and highlights the importance of the choice of the infrared cutoff function $R_k$.Christof Wetterich derived a new exact evolution equation for the scale dependence of an effective action, which is particularly useful for dealing with infrared problems in theories with massless modes in dimensions less than four. The equation for the effective potential allows for a useful truncation, making it applicable to high-temperature phase transitions in particle physics and critical exponent calculations in statistical mechanics. The evolution equation is expressed in terms of the exact propagator, which is the second functional derivative of the effective action. The equation is derived by adding a piece to the kinetic term and including sources, leading to a $k$-dependent generating functional. The evolution equation is shown to reduce to the one-loop equation under a suitable truncation, and it provides a systematic way to compute corrections to the one-loop results. The scale $k$ acts as an infrared cutoff, ensuring that large momentum contributions are exponentially suppressed. The author also discusses the conditions under which the equation holds and highlights the importance of the choice of the infrared cutoff function $R_k$.