Summary
Among seven problems, proposed for the XXI century by the Clay Mathematical Institute [1], there are two stemming from physics. One of them is called “Yang-Mills Existence and Mass Gap”. The detailed statement of the problem, written by A. Jaffe and E. Witten [2], gives both motivation and exposition of related mathematical results, known until now. Having some experience in the matter, I decided to complement their text by my own personal comments aimed mostly to mathematical audience.
The first variant was published in [3]. In this new version more details are given in the description of renormalization.
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References
Clay Mathematics Institute Millennium Prize Problems, http://www.claymath.org/prizeproblems/index.htm
A. Jaffe and E. Witten Quantum Yang-Mills Theory, http://www.claymath.org/prizeproblems/yang_mills.pdf
L. Faddeev: Bull. of Brazil Math. Soc.; New Series 33(2), 1
C._N. Yang, R. Mills: Phys. Rev. 96, 191 (1954)
R. Jackiw: What Good are Quantum Field Theory Infinities. In: Mathematical Physics 2000, ed by A. Fokas et al. (Imperial College Press, London 2000)
S. Coleman: Secret Symmetries: An Introduction to Spontaneous Symmetry Breakdown and Gauge Fields. In: Aspects of Symmetry, Selected Erice Lectures (Cambridge University Press, Cambridge 1985)
L. D. Faddeev, V. Popov: Phys. Lett. B 25, 29 (1967)
G. ’t Hooft: Nucl. Phys. B 33, 173 (1971)
L. D. Faddeev, A. A. Slavnov: Gauge Fields: An Introduction to Quantum Theory. In Frontiers in Physics, vol 83 (Addison-Wesley 1991)
M. E. Peskin, D. V. Schroeder: An Introduction to Quantum Field Theory (Addison-Wesley 1995)
F. A. Berezin: The Method of Secondary Quantization, (in russian), (Nauka, Moscow 1965)
D. Gross: The discovery of asymptotic freedom and the emergence of QCD. In: At the frontier of particle physics — Handbook of QCD, ed by M. Shifmann (World Scientific 2001)
L. Faddeev, A. J. Niemi: Phys. Lett. B 525, 195 (2002)
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Faddeev, L.D. (2005). Mass in Quantum Yang-Mills Theory (Comment on a Clay Millennium Problem). In: Benedicks, M., Jones, P.W., Smirnov, S., Winckler, B. (eds) Perspectives in Analysis. Mathematical Physics Studies, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-30434-7_6
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DOI: https://doi.org/10.1007/3-540-30434-7_6
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