Quasiclassical expansion of Yang-Mills heat kernels and approximate calculation of functional determinants

We find next-to-leading coefficients in the expansion of Sp exp(-tK) in powers of proper time t, where K is the differential operator for the gluon, ghost or fermion in a background Yang-Mills field. This expansion provides a possibility of estimating functional determinants in arbitrary background fields. For example, for the instanton background our very simple method gives the value of the determinants with an accuracy of a few percent, as compared to the labourious exact calculation.