Quantum equation of motion and two-loop cutoff renormalization for $\phi^3$ model

A. V. Ivanov   ; N. V. Kharuk

Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 26, Tome 487 (2019), pp. 151-166

Résumé

We present two-loop renormalization of $\phi^3$ model effective action by using the background field method and cutoff momentum regularization. In this paper we also study a derivation of the quantum equation of motion and its application to the renormalization procedure.

Bibliographie

[1] J. C. Collins, Renormalization: an introduction to renormalization, the renormalization group and the operator-product expansion, Cambridge University Press, Cambridge, 1984 | MR | Zbl

[2] J. C. Collins, DAMPT preprint 73/38

[3] A. J. Macfarlane, G. Woo, “$\Phi^3$ theory in six dimensions and the renormalization group”, Nuclear Physics B, 77 (1974), 91–108 | DOI

[4] J. L. Cardy, “High-energy behaviour in $\phi^3$ theory in six dimensions”, Nucl. Phys. B, 93 (1975), 525–546 | DOI

[5] R. W. Brown, L. B. Gordon, T. F. Wong, B. L. Young, “High-energy behavior of $\phi^3$ theory in six dimensions”, Physical Review D, 11 (1975), 2209–2218 | DOI

[6] A. J. McKane, D. J. Wallace, R. K. P. Zia, “Models for strong interactions in $6-\epsilon$ dimensions”, Physics Letters B, 65 (1976), 171–173 | DOI

[7] S. J. Chang, Y. P. Yao, “Nonperturbative approach to infrared behavior for $(\phi^3)_6$ theory and a mechanism of confinement”, Physical Review D, 16 (1977), 2948–2966 | DOI

[8] R. Gass, M. Dresden, “Puzzling Aspect of Quantum Field Theory in Curved Space-Time”, Physical Review Letters, 54 (1985), 2281–2284 | DOI | MR

[9] L. Culumovic, D. G. C. McKeon, T. N. Sherry, “Operator Regularization and the Renormalization Group to Two-Loop Order in $\phi^3_6$”, Annals of Physics, 197 (1990), 94–118 | DOI | MR | Zbl

[10] J. A. Gracey, “Four loop renormalization of $\phi^3$ theory in six dimensions”, Physical Review D, 92 (2015), 025012 | DOI | MR

[11] L. F. Abbott, “Introduction to the Background Field Method”, Acta Phys. Polon. B, 13 (1982), 33 | MR

[12] I. Y. Aref eva, A. A. Slavnov, L. D. Faddeev, “Generating functional for the S matrix in gauge-invariant theories”, Theor. Math. Phys., 21 (1974), 1165–1172 | DOI

[13] L. D. Faddeev, A. A. Slavnov, “Gauge Fields. Introduction To Quantum Theory”, Front. Phys., 50 (1980) ; Front. Phys., 83 (1990) | MR | Zbl

[14] L. D. Faddeev, Mass in Quantum Yang-Mills Theory: Comment on a Clay Millenium problem, 2009, arXiv: 0911.1013 [math-ph] | MR

[15] V. Fock, “Proper time in classical and quantum mechanics”, Phys. Z. Sowjetunion, 12 (1937), 404–425

[16] K. Hagiwara, S. Ishihara, R. Szalapski, D. Zeppenfeld, “Low energy effects of new interactions in the electroweak boson sector”, Phys. Rev. D, 48 (1993), 2182–2203 | DOI

[17] M. Harada, K. Yamawaki, “Wilsonian matching of effective field theory with underlying QCD”, Phys. Rev. D, 64 (2001), 014–023

[18] S. E. Derkachev, A. V. Ivanov, L. D. Faddeev, “Renormalization scenario for the quantum Yang Mills theory in four-dimensional space time”, Theoret. and Math. Phys., 192:2 (2017), 1134–1140 | DOI | MR | Zbl

[19] B. S. DeWitt, Dynamical Theory of Groups and Fields, Gordon and Breach, New York, 1965 | MR

[20] M. Ljscher, “Dimensional regularisation in the presence of large background fields”, Annals of Physics, 142 (1982), 359–392 | DOI | MR

[21] P. B. Gilkey, “The spectral geometry of a Riemannian manifold”, J. Differ. Geom., 10 (1975), 601–618 | DOI | MR | Zbl

[22] A. V. Ivanov, “Diagram technique for the heat kernel of the covariant Laplace operator”, Theoret. and Math. Phys., 198:1 (2019), 100–117 | DOI | MR | Zbl

[23] A. V. Ivanov, N. V. Kharuk, Heat kernel: proper time method, Fock-Schwinger gauge, path integral representation, and Wilson line, 2019, arXiv: 1906.04019 [hep-th]