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 TMF, 1983, Volume 56, Number 1, Pages 15–30 (Mi tmf2186)

The $CP^{N-1}$ model: Calculation of anomalous dimensions and the mixing matrices in the order $1/N$

A. N. Vasil'ev, M. Yu. Nalimov

Abstract: In the first order in $1/N$ for arbitrary dimension $2<d<4$ of space for the $CP^{N-1}$ model quantized by means of the auxiliary fields $\varphi$ and $B$ ($\Phi$ is the principal field, go the auxiliary scalar field, and $B$ the auxiliary vector field) the following are calculated: 1) the matrix of renormalization constants and the corresponding matrix of the anomalous dimensions of the mixed operators $\varphi$ and $B^2$ of canonical dimension $2$; 2) the analogous matrices for the mixed operators $\varphi^2$ and $F_{\alpha\beta}F_{\alpha\beta}$ of canonical dimension $4$, which determine two correction exponents $\omega$; 3) the anomalous dimension $\gamma_\Phi$ in an arbitrary gauge.

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English version:
Theoretical and Mathematical Physics, 1983, 56:1, 643–653

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Citation: A. N. Vasil'ev, M. Yu. Nalimov, “The $CP^{N-1}$ model: Calculation of anomalous dimensions and the mixing matrices in the order $1/N$”, TMF, 56:1 (1983), 15–30; Theoret. and Math. Phys., 56:1 (1983), 643–653

Citation in format AMSBIB
\Bibitem{VasNal83} \by A.~N.~Vasil'ev, M.~Yu.~Nalimov \paper The~$CP^{N-1}$ model: Calculation of anomalous dimensions and the mixing matrices in the order~$1/N$ \jour TMF \yr 1983 \vol 56 \issue 1 \pages 15--30 \mathnet{http://mi.mathnet.ru/tmf2186} \transl \jour Theoret. and Math. Phys. \yr 1983 \vol 56 \issue 1 \pages 643--653 \crossref{https://doi.org/10.1007/BF01027537} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983SA59100002} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. N. Vasil'ev, M. Yu. Nalimov, Yu. R. Khonkonen, “$1/N$ expansion: Calculation of anomalous dimensions and mixing matrices in the order $1/N$ for $N\times p$ matrix gauge-invariant $\sigma$-model”, Theoret. and Math. Phys., 58:2 (1984), 111–120
2. A. N. Vasil'ev, S. È. Derkachev, N. A. Kivel', A. S. Stepanenko, “Proof of conformal invariance in the critical regime for models of Gross–Neveu type”, Theoret. and Math. Phys., 92:3 (1992), 1047–1054
3. A. N. Vasil'ev, A. S. Stepanenko, “A method of calculating the critical dimensions of composite operators in the massless nonlinear $\sigma$ model”, Theoret. and Math. Phys., 95:1 (1993), 471–481
4. S. È. Derkachev, A. N. Manashov, “Critical dimensions of composite operators in the nonlinear $\sigma$-model”, Theoret. and Math. Phys., 116:3 (1998), 1034–1049
5. Ciuchini, M, “Quark mass anomalous dimension at O(1/N-f(2)) in QCD”, Physics Letters B, 458:1 (1999), 117
6. Ciuchini, M, “Computation of quark mass anomalous dimension at O(1/N-f(2)) in quantum chromodynamics”, Nuclear Physics B, 579:1–2 (2000), 56
7. Gracey J.A., “Large N-F Quantum Field Theory”, Int. J. Mod. Phys. A, 33:35 (2018), 1830032
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