A two-loop renormalization of φ3 model effective action is presented by using the background field method and cutoff momentum regularization. A derivation of the quantum equation of motion and its application to the renormalization procedure are also studied.
Similar content being viewed by others
References
J. C. Collins, Renormalization: an Introduction to Renormalization, the Renormalization Group and the Operator-Product Expansion, Cambridge University Press, Cambridge (1984).
J. C. Collins, DAMPT preprint 73/38.
A. J. Macfarlane and G. Woo, “Φ3 theory in six dimensions and the renormalization group,” Nucl. Phys. B, 77, 91–108 (1974).
J. L. Cardy, “High-energy behaviour in 𝜙3 theory in six dimensions,” Nucl. Phys. B, 93, 525–546 (1975).
R. W. Brown, L. B. Gordon, T. F. Wong, and B. L. Young, “High-energy behavior of 𝜙3 theory in six dimensions,” Phys. Rev. D, 11, 2209–2218 (1975).
A. J. McKane, D. J. Wallace, and R. K. P. Zia, “Models for strong interactions in 6 − 𝜖 dimensions,” Phys. Lett. B, 65, 171–173 (1976).
S. J. Chang and Y. P. Yao, “Nonperturbative approach to infrared behavior for (𝜙3)6 theory and a mechanism of confinement,” Phys. Rev. D, 16, 2948–2966 (1977).
R. Gass and M. Dresden, “Puzzling Aspect of Quantum Field Theory in Curved Space-Time,” Phys. Rev. Lett., 54, 2281–2284 (1985).
L. Culumovic, D. G. C. McKeon, and T. N. Sherry, “Operator Regularization and the Renormalization Group to Two-Loop Order in 𝜙36 ” Annals Phys., 197, 94–118 (1990).
J. A. Gracey, “Four loop renormalization of 𝜙3 theory in six dimensions,” Phys. Rev. D, 92, 025012 (2015).
L. F. Abbott, “Introduction to the Background Field Method,” Acta Phys. Polon. B, 13, 33 (1982).
I. Y. Arefeva, A. A. Slavnov, and L. D. Faddeev, “Generating functional for the S matrix in gauge-invariant theories,” Theor. Math. Phys., 21, 1165–1172 (1974).
L. D. Faddeev and A. A. Slavnov, “Gauge Fields. Introduction To Quantum Theory,” Front. Phys., 50 (1980), [Front. Phys. 83 (1990)].
L. D. Faddeev, “Mass in Quantum Yang-Mills Theory: Comment on a Clay Millenium problem,” arXiv:0911.1013 [math-ph] (2009).
V. Fock, “Proper time in classical and quantum mechanics,” Phys. Z. Sowjetunion, 12, 404–425 (1937).
K. Hagiwara, S. Ishihara, R. Szalapski, and D. Zeppenfeld, “Low energy effects of new interactions in the electroweak boson sector,” Phys. Rev. D, 48, 2182–2203 (1993).
M. Harada and K. Yamawaki, “Wilsonian matching of effective field theory with underlying QCD,” Phys. Rev. D, 64, 014–023 (2001).
S. E. Derkachev, A. V. Ivanov, and L. D. Faddeev, “Renormalization scenario for the quantum Yang Mills theory in four-dimensional space time,” Theor. Math. Phys., 192, No. 2, 1134–1140 (2017).
B. S. DeWitt, Dynamical Theory of Groups and Fields, Gordon and Breach, New York (1965).
M. Ljscher, “Dimensional regularisation in the presence of large background fields,” Annals Phys., 142, 359–392 (1982).
P. B. Gilkey, “The spectral geometry of a Riemannian manifold,” J. Diff. Geom., 10, 601–618 (1975).
A. V. Ivanov, “Diagram technique for the heat kernel of the covariant Laplace operator,” Theor. Math. Phys., 198, No. 1, 100–117 (2019).
A. V. Ivanov and N. V. Kharuk, “Heat kernel: proper time method, Fock-Schwinger gauge, path integral representation, and Wilson line,” arXiv:1906.04019 [hep-th] (2019).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 487, 2019, pp. 151–166.
Rights and permissions
About this article
Cite this article
Ivanov, A.V., Kharuk, N.V. Quantum Equation of Motion and Two-Loop Cutoff Renormalization for 𝜙3 Model. J Math Sci 257, 526–536 (2021). https://doi.org/10.1007/s10958-021-05500-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-021-05500-5