Abstract
We state some new results about the configuration space of pure Yang-Mills theory. These results come from the study of the kinetic energy term of the Lagrangian of the theory. This term defines a riemannian metric on the space of non-equivalent gauge potentials. We develop a riemannian calculus on the configuration space, compute the riemannian connection, the curvature tensor, and solve for the geodesics, etc. We show that the Gribov ambiguity is more than an artefact of the choice of a gauge condition, and is related to the existence of conjugate points on the geodesics, and is thus an intrinsic feature of the theory.
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Dirac, P.A.M.: In: Lectures on quantum mechanics. Belfer Series (1964)
Faddeev, L.D.: Theor. Math. Phys.1, 3 (1969)
Fradkin, E.S., Vilkovisky, G.S.: CERN Preprint TH 2332 (1977)
Babelon, O., Viallet, C.M.: Phys. Lett.85B, 246 (1979)
Faddeev, L.D., Popov, V.N.: Phys. Lett.25B, 29 (1967)
Asorey, M., Mitter, P.K.: Commun. Math. Phys.80, 43–58 (1981)
Daniel, M., Viallet, C.M.: Rev. Mod. Phys.52, 175–197 (1980)
Kobayashi, S., Nomizu, K.: In: Foundations of differential geometry, Vols. 1 and 2. New York: Wiley 1963, 1969
Atiyah, M.F., Hitchin, N., Singer, I.M.: Proc. Roy. Soc. LondonA362 125 (1978)
Bourguignon, J.P.: Comp. Math.30 1 (1975)
Singer, I.M.: Comm. Math. Phys.60 7 (1978)
Narasimhan, M.S., Ramadas, T.R.: Commun. Math. Phys.67 21 (1979)
Mitter, P.K., Viallet, C.M.: Commun. Math. Phys.79 457 (1981)
Communication given by J.S. Rogulsky, Seminar on Complex Analysis (Trieste 1980)
Daniel, M., Viallet, C.M.: Phys. Lett.76B 458 (1978)
Gribov, V.N.: In: Materials for the XII Winterschool of Leningrad (1977)
Bott, R.: In: Representation Theory of Lie groups. London Math. Soc. Lect. Notes34, C.U.P. (1979); see also de Witt, B.: Phys. Rev.160, 1113 (1967)
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Communicated by R. Stora
Laboratoire associé au CNRS
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Babelon, O., Viallet, C.M. The riemannian geometry of the configuration space of gauge theories. Commun.Math. Phys. 81, 515–525 (1981). https://doi.org/10.1007/BF01208272
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DOI: https://doi.org/10.1007/BF01208272