Schwinger function

In quantum field theory, the Wightman distributions can be analytically continued to analytic functions in Euclidean space with the domain restricted to ordered n-tuples in ${\displaystyle \mathbb {R} ^{d}}$ that are pairwise distinct.^[1] These functions are called the Schwinger functions (named after Julian Schwinger) and they are real-analytic, symmetric under the permutation of arguments (antisymmetric for fermionic fields), Euclidean covariant and satisfy a property known as reflection positivity. Properties of Schwinger functions are known as Osterwalder–Schrader axioms (named after Konrad Osterwalder and Robert Schrader).^[2] Schwinger functions are also referred to as Euclidean correlation functions.