Geodesic
Wilson expansion for chiral field
Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 1, pp. 24-31
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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. 
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     author = {I. Ya. Aref'eva},
     title = {Wilson expansion for chiral field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {24--31},
     year = {1978},
     volume = {36},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1978_36_1_a1/}
}
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I. Ya. Aref'eva. Wilson expansion for chiral field. Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 1, pp. 24-31. http://geodesic.mathdoc.fr/item/TMF_1978_36_1_a1/

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