Spectral Boundary Conditions in One-Loop Quantum Cosmology

Details Spectral Boundary Conditions in One-Loop Quantum Cosmology Spectral Boundary Conditions in One-Loop Quantum Cosmology

1995-07-04

arxiv.org/abs/gr-qc/9507005v1

Phys.Rev. D44 (1991) 1713-1721

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

29 pages, plain-tex, published in Physical Review D, volume 44, pages 1713-1721, year 1991

Scientific paper

10.1103/PhysRevD.44.1713

For fermionic fields on a compact Riemannian manifold with boundary one has a choice between local and non-local (spectral) boundary conditions. The one-loop prefactor in the Hartle-Hawking amplitude in quantum cosmology can then be studied using the generalized Riemann zeta-function formed from the squared eigenvalues of the four-dimensional fermionic operators. For a massless Majorana spin-1/2 field, the spectral conditions involve setting to zero half of the fermionic field on the boundary, corresponding to harmonics of the intrinsic three-dimensional Dirac operator on the boundary with positive eigenvalues. Remarkably, a detailed calculation for the case of a flat background bounded by a three-sphere yields the same value zeta(0)=11/360 as was found previously by the authors using local boundary conditions. A similar calculation for a spin-3/2 field, working only with physical degrees of freedom (and, hence, excluding gauge and ghost modes, which contribute to the full Becchi-Rouet-Stora-Tyutin-invariant amplitude), again gives a value zeta(0)=-289/360 equal to that for the natural local boundary conditions.

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