Reflection positivity is a positivity condition on the correlation functions of a Euclidean quantum field theory. Let
denote the antilinear operator on complex-valued functionals
obtained by reflecting the Euclidean time coordinate and complex-conjugating scalar
coefficients. In a functional integral formulation,
the condition requires
 |
for suitable functionals 
supported at positive Euclidean times. The antilinearity of
makes 
a sesquilinear form on such functionals, and
reflection positivity requires 
.
Reflection positivity is the positivity axiom in the Osterwalder-Schrader axioms. It makes the associated quadratic form a positive semidefinite quadratic form. After quotienting its null space, the form induces an inner product on the reconstructed state space, which is essential for obtaining a quantum theory on Minkowski space from its Schwinger functions.
