Related papers: Non-Locality and Ellipticity in a Gauge-Invariant …
The quantum theory of a free particle on a portion of two-dimensional Euclidean space bounded by a circle and subject to non-local boundary conditions gives rise to bulk and surface states. Starting from this well known property, a…
Recent work in the literature has proposed the use of non-local boundary conditions in Euclidean quantum gravity. The present paper studies first a more general form of such a scheme for bosonic gauge theories, by adding to the boundary…
Maxwell theory can be studied in a gauge which is invariant under conformal rescalings of the metric, and first proposed by Eastwood and Singer. This paper studies the corresponding quantization in flat Euclidean 4-space. The resulting…
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…
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…
Zeta-function regularization is applied to complete a recent analysis of the quantized electromagnetic field in the presence of boundaries. The quantum theory is studied by setting to zero on the boundary the magnetic field, the…
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…
The quantisation of gauge theories usually procedes through the introduction of ghost fields and BRST symmetry. In the case of quantum gravity in the presence of boundaries, the BRST-invariant boundary value problem for the gauge field…
This paper reviews the progress made over the last five years in studying boundary conditions and semiclassical properties of quantum fields about 4-real-dimensional Riemannian backgrounds. For massless spin-${1\over 2}$ fields one has a…
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…
This paper describes recent progress in the analysis of relativistic gauge conditions for Euclidean Maxwell theory in the presence of boundaries. The corresponding quantum amplitudes are studied by using Faddeev-Popov formalism and…
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…
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.…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
Recent work in the literature has studied a new set of local boundary conditions for the quantized gravitational field, where the spatial components of metric perturbations, and ghost modes, are subject to Robin boundary conditions, whereas…
We study the solvability of boundary-value problems for differential-operator equations of the second order in L p (0, 1; X), with 1 < p < +$\infty$, X being a UMD complex Banach space. The originality of this work lies in the fact that we…
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…
In this thesis quantum gauge theories are considered in the framework of local, causal perturbation theory. Gauge invariance is described in terms of the BRS formalism. Local interacting field operators are constructed perturbatively and…
The bulk (Einstein-Hilbert) and boundary (Gibbons-Hawking) terms in the gravitational action are generally renormalized differently when integrating out quantum fluctuations. The former is affected by nonminimal couplings, while the latter…
We consider second order elliptic operators with real, nonsymmetric coefficient functions which are subject to mixed boundary conditions. The aim of this paper is to provide uniform resolvent estimates for the realizations of these…