Schwinger's quantum action principle

The Schwinger's quantum action principle is a variational approach to quantum mechanics and quantum field theory. This theory was introduced by Julian Schwinger. In this approach, the quantum action is an operator. Although it is superficially different from the path integral formulation where the action is a classical function, the modern formulation of the two formalisms are identical.

Suppose we have two states defined by the values of a complete set of commuting operators at two times. Let the early and late states be ${\displaystyle |A\rangle }$ and ${\displaystyle |B\rangle }$, respectively. Suppose that there is a parameter in the Lagrangian which can be varied, usually a source for a field. The main equation of Schwinger's quantum action principle is:

where the derivative is with respect to small changes in the parameter.

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