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Euclidean Action

The Euclidean action S_E of a physical system is the action obtained after replacing real time by imaginary time, a form of analytic continuation called Wick rotation. In Euclidean quantum field theory, a scalar field with potential V has the formal action

S_E[phi]=int[1/2(del phi)^2+V(phi)]d^dx.

The Euclidean functional-integral weight is exp(-S_E), rather than the oscillatory real-time weight exp(iS). This change is one reason Euclidean formulations connect quantum field theory with probability and statistical mechanics.

See also

Action, Analytic Continuation, Euclidean Quantum Field Theory, Functional Integral, Partition Function

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References

Glimm, J. and Jaffe, A. Quantum Physics: A Functional Integral Point of View, 2nd ed. New York: Springer-Verlag, 1987.

Cite this as:

Weisstein, Eric W. "Euclidean Action." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EuclideanAction.html

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