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.
Journal of Cosmology and Astroparticle Physics
- Pub Date:
- April 2011
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology;
- Mathematical Physics
- LaTex, 15 pages, a new section is added, containing the discussion of a special case of the operator having the second zero mode, typos are corrected