On the functional determinant of a special operator with a zero mode in cosmology

Details On the functional determinant of a special operator with a zero mode in cosmology On the functional determinant of a special operator with a zero mode in cosmology

2010-12-07

arxiv.org/abs/1012.1571v2

JCAP 1104:035,2011

Physics

High Energy Physics

High Energy Physics - Theory

LaTex, 15 pages, a new section is added, containing the discussion of a special case of the operator having the second zero mo

Scientific paper

10.1088/1475-7516/2011/04/035

The functional determinant of a special second order quantum-mechanical operator is calculated with its zero mode gauged out by the method of the Faddeev-Popov gauge fixing procedure. This operator subject to periodic boundary conditions arises in applications of the early Universe theory and, in particular, determines the one-loop statistical sum in quantum cosmology generated by a conformal field theory (CFT). The calculation is done for a special case of a periodic zero mode of this operator having two roots (nodes) within the period range, which corresponds to the class of cosmological instantons in the CFT driven cosmology with one oscillation of the cosmological scale factor of its Euclidean Friedmann-Robertson-Walker metric.

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