On the zero modes of the Faddeev-Popov operator in the Landau gauge

Journal Article · Sat Feb 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4865424· OSTI ID:22251408

Vilar, L. C. Q.,; Lemes, V. E. R., ^[1]

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1. Instituto de Física, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, Maracanã, Rio de Janeiro, RJ 20550-013 (Brazil)

Following Henyey procedure [Phys. Rev. D 20, 1460 (1979)], we construct examples of zero modes of the Faddeev-Popov operator in the Landau gauge in Euclidean space in D dimensions, for both SU(2) and SU(3) groups. We obtain gauge field configurations A{sub μ}{sup a} which give rise to a field strength, F{sub μν}{sup a}=∂{sub μ}A{sub ν}{sup a}−∂{sub ν}A{sub μ}{sup a}+f{sup abc}A{sub μ}{sup b}A{sub ν}{sup c}, whose nonlinear term, f{sup abc}A{sub μ}{sup b}A{sub ν}{sup c}, turns out to be non-vanishing. To our knowledge, this is the first time where such a non-abelian configuration is explicitly obtained in the case of SU(3) in 4D.

• OSTI ID: 22251408
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
EUCLIDEAN SPACE
GAUGE INVARIANCE
NONLINEAR PROBLEMS
SU-3 GROUPS