Abstract
The functional determinant of a special second orderquantum-mechanical operator is calculated with its zero mode gaugedout by the method of the Faddeev-Popov gauge fixing procedure. Thisoperator subject to periodic boundary conditions arises inapplications of the early Universe theory and, in particular,determines the one-loop statistical sum in quantum cosmologygenerated by a conformal field theory (CFT). The calculation is donefor a special case of a periodic zero mode of this operator havingtwo roots (nodes) within the period range, which corresponds to theclass of cosmological instantons in the CFT driven cosmology withone oscillation of the cosmological scale factor of its EuclideanFriedmann-Robertson-Walker metric.
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