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Invariance principles determine many key properties in quantum field theory, including, in particular, the appropriate form of the boundary conditions. A crucial consistency check is the proof that the resulting boundary-value problem is…
Boundary conditions play a crucial role in the path-integral approach to quantum gravity and quantum cosmology, as well as in the current attempts to understand the one-loop semiclassical properties of quantum field theories. Within this…
A general method exists for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at one-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen…
A general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at one-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h…
Gauge-invariant boundary conditions in Euclidean quantum gravity can be obtained by setting to zero at the boundary the spatial components of metric perturbations, and a suitable class of gauge-averaging functionals. This paper shows that,…
We review what is known about boundary conditions in General Relativity on a spacetime of Euclidean signature. The obvious Dirichlet boundary condition, in which one specifies the boundary geometry, is actually not elliptic and in general…
A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral…
The axial gauge is applied to the analysis of Euclidean quantum gravity on manifolds with boundary. A set of boundary conditions which are completely invariant under infinitesimal diffeomorphisms require that spatial components of metric…
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…
The boundary-value problem for Laplace-type operators acting on smooth sections of a vector bundle over a compact Riemannian manifold with generalized local boundary conditions including both normal and tangential derivatives is studied.…
The Euclidean path integral for gravity is enriched by the addition of boundaries, which provide useful probes of thermodynamic properties. Common boundary conditions include Dirichlet conditions on the boundary induced metric;…
We consider four-dimensional Euclidean gravity in a finite cavity. Dirichlet conditions do not yield a well-posed elliptic system, and Anderson has suggested boundary conditions that do. Here we point out that there exists a one-parameter…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
A vanishing one-loop wave function of the Universe in the limit of small three-geometry is found, on imposing diffeomorphism-invariant boundary conditions on the Euclidean 4-ball in the de Donder gauge. This result suggests a quantum…
When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential…
The fundamental laws of physics can be derived from the requirement of invariance under suitable classes of transformations on the one hand, and from the need for a well-posed mathematical theory on the other hand. As a part of this…
A key problem in the attempt to quantize the gravitational field is the choice of boundary conditions. These are mixed, in that spatial and normal components of metric perturbations obey different sets of boundary conditions. In the…
When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential…
Non-local boundary conditions for Euclidean quantum gravity are proposed, consisting of an integro-differential boundary operator acting on metric perturbations. In this case, the operator P on metric perturbations is of Laplace type,…
This paper studies the linearized gravitational field in the presence of boundaries. For this purpose, $\zeta$-function regularization is used to perform the mode-by-mode evaluation of BRST-invariant Faddeev-Popov amplitudes in the case of…