New spectral representation and evaluation of fπ and the quark condensate ⟨(q)over-barq⟩ in the terms of string tension

New spectral representations for f(pi) and chiral condensate are derived in QCD and Used for calculations in the large-N-c limit. Both quantities are expressed in this limit through string tension sigma and gluon correlation length T-g without fitting parameters. As a result, one obtains ((q) over barq) = -N(c)sigma(2)T(g)a1, f(pi) = rootN(c)sigmaT(g)a(2), with a(1) = 0.0823, a(2) = 0.30. Taking sigma = 0.18 GeV2 and T-g = 1 GeV-1, as known from analytic and lattice calculations, this yields ((q) over barq)(mu = 2 GeV) = -(0.225 GeV)(3), f(pi) = 0.094 GeV, which is close to the standard Values. (C) 2004 MAIK Nauka/Interperiodica.