Geodesic
Renormalization-group approach in the theory of turbulence: The dimensions of composite operators
Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 2, pp. 268-281 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the framework of the renormalization-group approach in the theory of turbulence proposed by De Dominieis and Martin [1], the problem of renormalization and determination of the critical dimensions of composite operators is discussed. The renormalization of the system of operators of canonical dimension $4$, which includes the operator $F=\varphi\Delta\varphi$, where $\varphi$ is the velocity field, is considered. It is shown that the critical dimension $\Delta_F$ associated with this operator is exactly equal to the Kolmogorov dimension: $\Delta_F=0$. The Appendix gives brief proofs of, first, a theorem on the equivalence of an arbitrary stochastic problem and quantum field theory and, second, a theorem that determines the restriction of the Green's functions of a stochastic problem to a simultaneity surface. 
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     title = {Renormalization-group approach in the theory of turbulence: {The} dimensions of composite operators},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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L. Ts. Adzhemyan; A. N. Vasil'ev; Yu. M. Pis'mak. Renormalization-group approach in the theory of turbulence: The dimensions of composite operators. Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 2, pp. 268-281. http://geodesic.mathdoc.fr/item/TMF_1983_57_2_a10/

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[3] Parisi G., Wu Y. S., Scientia Sinica, 24 (1981), 483–488 | MR

[4] Alfaro J., Sakita B., Derivation of quenched momentum prescription by means of stochastic quantization, Preprint CCNY-HEP-82/8, CUNY, New-York, 1982 | MR

[5] Floratos E., Iliopoulos J., Equivalence of stochastic and canonical quantization in perturbation theory, Preprint LPTENS 82/31, LPTENS, Paris, 1982 | MR

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