Operator product expansion and non-perturbative renormalization
نویسندگان
چکیده
Here A, B, and C are operators; W C (x − y) are c-number functions (Wilson coefficients), singular when |x − y| → 0, that can be computed, for example, in perturbation theory. Dimensional analysis tells us that the leading contribution for y → x is due to the operators C’s in Eq. (1) that have the lowest dimension. Notice that the OPE is an operator relation and therefore, for any matrix element 〈ψ|A(x)B(y)|φ〉, the coefficients W C (x − y) are independent of the states |ψ〉 and |φ〉. This also means that if one wants to use the OPE, one should go through all the subtleties in the definition of the operators in quantum field theory (regularization, renormalization, . . . ). The authors of reference [1] have proposed to consider, for lattice applications, the OPE in the particular case in which A and B are the components of a conserved current Jμ. This case is particularly simple because the components of Jμ do not need to be renormalized. This means that
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