Classical mechanics (and classical field theory) has the principle of stationary action (Hamilton's principle) as main principle. The Euler-Lagrange equations are derived from that principle, by using calculus of variations, on functionals (functions of functions).

Is there an equivalent principle of stationary action for QFT? I understand that the Schwinger-Dyson equations are the "equivalent" of the Euler-Lagrange equations, but instead of being differential equations in 1 (or 4) variables, the variable is a function itself (infinite dimensional).

I imagine that if the analogy works out, one should use functions of functionals (functions of functions of functions). Or maybe the "principle for QFT" does not look like a principle of stationary action at all.

So, is there some kind of "principle" that gives the Schwinger-Dyson equations in QFT, in the same way the principle of stationary action gives the Euler-Lagrange equations for classical field theory?

Is there an equivalent principle of stationary action for QFT? I understand that the Schwinger-Dyson equations are the "equivalent" of the Euler-Lagrange equations, but instead of being differential equations in 1 (or 4) variables, the variable is a function itself (infinite dimensional).

I imagine that if the analogy works out, one should use functions of functionals (functions of functions of functions). Or maybe the "principle for QFT" does not look like a principle of stationary action at all.

So, is there some kind of "principle" that gives the Schwinger-Dyson equations in QFT, in the same way the principle of stationary action gives the Euler-Lagrange equations for classical field theory?

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