Abstract
We present methodological proposals regarding the definition of the notion of the effective action, the coupling constant renormalization, and the interpretation of dimensional transmutation. We show that the divergences that arise when quantizing a Yang-Mills field can be eliminated and lead to violation of the scaling invariance of the classical theory.
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A. A. Slavnov and L. D. Faddeev, Introduction to the Quantum Theory of Gauge Fields [in Russian], Nauka, Moscow (1988); English transl.: Gauge Fields: An Introduction to Quantum Theory (Frontiers Phys., Vol. 83), Westview, Boulder, Colo. (1993).
L. D. Faddeev, Bull. Braz. Math. Soc., n.s., 33, 201–212 (2002); arXiv:0911.1013v1 [math-ph] (2009).
L. D. Faddeev, “Separation of scattering and selfaction revisited,” arXiv:1003.4854v1 [hep-th] (2010).
L. D. Faddeev, Theor. Math. Phys., 148, 986–994 (2006).
V. Fock, Phys. Z. Sowjetunion, 12, 404–425 (1937).
I. Jack and H. Osborn, Nucl. Phys. B, 207, 474–504 (1982).
L. D. Faddeev, “Knots as possible excitations of the quantum Yang-Mills fields,” in: Quantum Field Theory and Beyond: Essays in Honor of Wolfhart Zimmermann (E. Seiler, K. Sibold, eds.), World Scientific, Hackensack, N. J. (2008), pp. 156–166; arXiv:0805.1624v1 [hep-th] (2008).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 181, No. 3, pp. 597–602, December, 2014.
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Faddeev, L.D. A couple of methodological comments on the quantum Yang-Mills theory. Theor Math Phys 181, 1638–1642 (2014). https://doi.org/10.1007/s11232-014-0240-4
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DOI: https://doi.org/10.1007/s11232-014-0240-4