Wilson expansion for chiral field

It is suggested that instead of the classical chirality condition $n^2(x)=\textrm{const}$, which is meaningless in quantum field theory, a Wilson expansion of special form $(n(x),n(x+\varepsilon))=C(\varepsilon)+R(x,\varepsilon)$, where $C(\varepsilon)$ is a $c$-number and $R(x,\varepsilon)\to 0$ as $\varepsilon\to 0$, should be considered. It is shown that this quantum chirality condition is satisfied in the previously constructed [1, 2] renormalized perturbation theory in $1/N$ for dimensions $D=2$ and $3$ of spacetime. For $D=4$, the Chirality condition is violated although the constructed theory is finite. The quantum chirality condition has the consequence that for $D=2$ and $3$ the renormalizations reduce to renormalizations of only the charge and the wave function.