Geodesic
Nontrivial quantization of $\phi^4_n$, $n\ge2$
Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 1, pp. 103-111

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The conventional quantization of covariant $\phi^4_n$ scalar field models for space–time dimensions $n\ge5$ is trivial, and this may also be true for $n=4$. But an alternative $O(\hbar)$ counterterm leads to nontrivial results for all $n\ge4$ and also provides a different quantization for $n=2,3$. We determine the counterterm that provides these desirable properties as simply and directly as possible. The same counterterm also resolves models such as $\phi^p_n$ for all even $p$ including those where $p>2n/(n-2)$, which are traditionally regarded as nonrenormalizable.
Keywords: nontriviality of phi to the fourth, overcoming nonrenormalizability, mixed model. 
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     author = {J. R. Klauder},
     title = {Nontrivial quantization of $\phi^4_n$, $n\ge2$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {103--111},
     publisher = {mathdoc},
     volume = {182},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a5/}
}
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J. R. Klauder. Nontrivial quantization of $\phi^4_n$, $n\ge2$. Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 1, pp. 103-111. http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a5/