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
where Euclidean action and
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 Analytic Continuation ,
Euclidean Action ,
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. 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 https://mathworld.wolfram.com/EuclideanQuantumFieldTheory.html
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is the Euclidean action and 
is the corresponding partition function.
