In quantum field theory, the effective action is a modified expression for the action, which takes into account quantum-mechanical corrections, in the following sense:
In classical mechanics, the equations of motion can be derived from the action by the principle of stationary action. This is not the case in quantum mechanics, where the amplitudes of all possible motions are added up in a path integral. However, if the action is replaced by the effective action, the equations of motion for the vacuum expectation values of the fields can be derived from the requirement that the effective action be stationary. For example, a field with a potential, at a low temperature, will not settle in a local minimum of, but in a local minimum of the effective potential which can be read off from the effective action.
Furthermore, the effective action can be used instead of the action in the calculation of correlation functions, and then only tree diagrams should be taken into account.
Read more about Effective Action: Mathematical Details, One Loop Approximation
Famous quotes containing the words effective and/or action:
“Justice in the hands of the powerful is merely a governing system like any other. Why call it justice? Let us rather call it injustice, but of a sly effective order, based entirely on cruel knowledge of the resistance of the weak, their capacity for pain, humiliation and misery. Injustice sustained at the exact degree of necessary tension to turn the cogs of the huge machine-for- the-making-of-rich-men, without bursting the boiler.”
—Georges Bernanos (1888–1948)
“The moment we choose to love we begin to move against domination, against oppression. The moment we choose to love we begin to move towards freedom, to act in ways that liberate ourselves and others. That action is the testimony of love as the practice of freedom.”
—bell hooks (b. c. 1955)