Related papers: Boundary Operators in Euclidean Quantum Gravity
Eigenvalue problems for semidefinite operators with infinite dimensional kernels appear for instance in electromagnetics. Variational discretizations with edge elements have long been analyzed in terms of a discrete compactness property. As…
For vacuum Maxwell theory in four dimensions, a supplementary condition exists (due to Eastwood and Singer) which is invariant under conformal rescalings of the metric, in agreement with the conformal symmetry of the Maxwell equations.…
We propose and develop a general algorithm for finding the action for cosmological perturbations which rivals the conventional, gauge-invariant approach and can be applied to theories with more than one metric. We then apply it to a…
On the path towards quantum gravity, we find friction between temporal relations in quantum mechanics (QM) (where they are fixed and field-independent), and in general relativity (where they are field-dependent and dynamic). This paper aims…
The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…
BRST-invariant action of general relativity in the unimodular gauge proposed by Baulieu is studied without using perturbative expansions. The expression for the path integral in the unimodular gauge is reduced to a form in which a…
This article offers a study of the Calder\'on type inverse problem of determining up to second order coefficients of the higher order elliptic operator. Here we show that it is possible to determine an anisotropic second order perturbation…
Perturbative canonical quantum gravity is considered, when coupled to a renormalizable model for matter fields. It is proposed that the functional integral over the dilaton field should be disentangled from the other integrations over the…
We study infinite weighted graphs with view to \textquotedblleft limits at infinity,\textquotedblright or boundaries at infinity. Examples of such weighted graphs arise in infinite (in practice, that means \textquotedblleft…
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…
We study the obstacle problem for fully nonlinear elliptic operators with an anisotropic degeneracy on the gradient: \[ \min \left\{f-|Du|^\gamma F(D^2u),u-\phi\right\} = 0 \quad\textrm{ in }\quad \Omega. \] We obtain existence of solutions…
We study gauge theories with/without an extra dimension at finite temperature, in which there are two kinds of order parameters of gauge symmetry breaking. The one is the zero mode of the gauge field for the Euclidean time direction and the…
We present a constructive method to devise boundary conditions for solutions of second-order elliptic equations so that these solutions satisfy specific qualitative properties such as: (i) the norm of the gradient of one solution is bounded…
It is shown that if the Euclidean path integral measure of a minimally coupled free quantum scalar field on a classical metric background is interpreted as probability of observing the field configuration given the background metric then…
In this paper we study boundary value problems for higher order elliptic differential operators in divergence form. We consider the two closely related topics of inhomogeneous problems and problems with boundary data in fractional…
We develop an elliptic theory based in $L^2$ of boundary value problems for general wedge differential operators of first order under only mild assumptions on the boundary spectrum. In particular, we do not require the indicial roots to be…
We propose that quantum physics is the continuous approximation of a more fundamental, discrete graph theory (theory X). Accordingly, the Euclidean transition amplitude Z provides a partition function for geometries over the graph, which is…
We study quantum field theories with boundary by utilizing non-invertible symmetries. We consider three kinds of boundary conditions of the four dimensional $\mathbb{Z}_2$ lattice gauge theory at the critical point as examples. The weights…
We discuss some aspects of the metric configuration space in quantum gravity in the background field formalism. We give a necessary and sufficient condition for the parameterization of Euclidean metric fluctuations such that i) the…
The G-->0 limit of Euclidean gravity introduced by Smolin is described by a generally covariant U(1)xU(1)xU(1) gauge theory. In an earlier paper, Tomlin and Varadarajan constructed the quantum Hamiltonian constraint of density weight 4/3…