Non-Local Properties in Euclidean Quantum Gravity

Abstract

In the one-loop approximation for Euclidean quantum gravity, the boundary conditions which are completely invariant under gauge transformations of metric perturbations involve both normal and tangential derivatives of the metric perturbations $h_{00}$ and $h_{0i}$, while the $h_{ij}$ perturbations and the whole ghost one-form are set to zero at the boundary. The corresponding one-loop divergency for pure gravity has been recently evaluated by means of analytic techniques. It now remains to compute the contribution of all perturbative modes of gauge fields and gravitation to the one-loop effective action for problems with boundaries. The functional determinant has a non-local nature, independently of boundary conditions. Moreover, the analysis of one-loop divergences for supergravity with non-local boundary conditions has not yet been completed and is still under active investigation.

11 pages, plain-tex, revised version, to appear in Proceedings of the Third Workshop on Quantum Field Theory under the Influence of External Conditions (Leipzig, 18-22 September 1995). In the revised version, the presentation has been improved

References in corpus (17)

• Elementary gates for quantum computation
• Heat-kernel coefficients of the Laplace operator on the D-dimensional ball
• One-Loop Amplitudes in Euclidean Quantum Gravity
• Local Boundary Conditions for the Dirac Operator and One-Loop Quantum Cosmology
• Spectral Boundary Conditions in One-Loop Quantum Cosmology
• Conformal anomalies on Einstein spaces with Boundary
• Euclidean Maxwell Theory in the Presence of Boundaries. II
• Gravitons in One-Loop Quantum Cosmology: Correspondence Between Covariant and Non-Covariant Formalisms
• Further functional determinants
• Diffeomorphism invariant eigenvalue problem for metric perturbations in a bounded region
• Relativistic Gauge Conditions in Quantum Cosmology
• One-loop effective potential for SO(10) GUT theories in de Sitter space
• Gauge-Averaging Functionals for Euclidean Maxwell Theory in the Presence of Boundaries
• Heat-kernel coefficients and functional determinants for higher-spin fields on the ball
• Spontaneously Broken SU(5) Symmetries and One-Loop Effects in the Early Universe
• Cosmological Restrictions on Conformally Invariant SU(5) GUT Models
• Local Supersymmetry in One-Loop Quantum Cosmology

Cited by in corpus (2)

• Spectral invariants for the Dirac equation on the d-Ball with various boundary conditions
• Essential self-adjointness in one-loop quantum cosmology