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Euclidean Quantum Field Theory

Euclidean quantum field theory is the formulation of quantum field theory on Euclidean space, rather than on Lorentzian spacetime. It is commonly obtained from a Lorentzian theory by analytic continuation of the time coordinate. Its correlation functions, called Schwinger functions, can be represented formally by functional integrals with an exponentially decaying weight

<O>=1/ZintO[phi]e^(-S[phi])Dphi,

where S is the Euclidean action and Z is the corresponding partition function.

The Osterwalder-Schrader axioms give conditions under which Euclidean correlation functions reconstruct a quantum field theory on Minkowski space (Osterwalder and Schrader 1973, 1975). This makes Euclidean quantum field theory useful both as a mathematical definition and as a computational tool.

See also

Euclidean Space, Functional Integral, Minkowski Space, Osterwalder-Schrader Axioms, Quantum Field Theory

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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.Osterwalder, K. and Schrader, R. "Axioms for Euclidean Green's Functions." Comm. Math. Phys. 31, 83-112, 1973. https://doi.org/10.1007/BF01645738.Osterwalder, K. and Schrader, R. "Axioms for Euclidean Green's Functions. II." Comm. Math. Phys. 42, 281-305, 1975. https://doi.org/10.1007/BF01608978.

Cite this as:

Weisstein, Eric W. "Euclidean Quantum Field Theory." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EuclideanQuantumFieldTheory.html

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