Related papers: Two-boundary problems in Euclidean quantum gravity
In canonical quantum gravity, when space is a compact manifold with boundary there is a Hamiltonian given by an integral over the boundary. Here we compute the action of this `boundary Hamiltonian' on observables corresponding to open…
We study small perturbations of the Dirichlet problems for second order elliptic equations that degenerate on the boundary. The limit of the solution, as the perturbation tends to zero, is calculated. The result is based on a certain…
We derive the conditions for a non-equatorial eccentric bound orbit to exist around a Kerr black hole in two-parameter spaces: the energy, angular momentum of the test particle, spin of the black hole, and Carter's constant space ($E$, $L$,…
In loop quantum gravity the discrete nature of quantum geometry acts as a natural regulator for matter theories. Studies of quantum field theory in quantum space-times in spherical symmetry in the canonical approach have shown that the main…
In this paper, we consider a family of second-order elliptic systems subject to a periodically oscillating Robin boundary condition. We establish the qualitative homogenization theorem on any Lipschitz domains satisfying a non-resonance…
We study quantum mechanical systems with "spin"-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the…
We attempt to clarify several aspects concerning the recently presented four-dimensional Einstein-Gauss-Bonnet gravity. We argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020)] generally involves ill-defined…
Bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ are investigated. We impose the Neumann boundary condition on the two concentric windows of the radii $a$ and $ b$ located…
We study wormhole as the solution of the Wheeler-deWitt (WdW ) equation satisfying Hawking-Page wormhole boundary conditions in Friedmann-Robertson-Walker (FRW) cosmology. The quantum wormholes are formulated with arbitrary factor ordering…
We introduce Robin boundary conditions for biharmonic operators, which are a model for elastically supported plates and are closely related to the study of spaces of traces of Sobolev functions. We study the dependence of the operator, its…
We consider perturbations in the fields of the 't Hooft-Polyakov monopole, dyon and point electric solutions. We find a series of bound modes where the fields are confined to the core of the respective solutions, and these are interpreted…
The so-called two-vertex model of loop quantum gravity has been analytically studied in the past within a U($N$) symmetry-reduced sector leading to a cosmological interpretation. In this work we study the simplest non-trivial two-vertex…
We consider singular perturbed eigenvalue problem for Laplace operator in a two-dimensional domain. In the boundary we select a set depending on a character small parameter and consisting of a great number of small disjoint parts. On this…
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…
For a bounded domain $\Omega$ with a piecewise smooth boundary in an $n$-dimensional Euclidean space $\mathbf{R}^{n}$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. First we give a general inequality for…
A new method to compute the symplectic structure of a quantum field theory with non trivial boundary conditions is proposed. Following the suggestion in \cite{ho:gnus, ardalan}, we regard that the boundary conditions are second class…
We study point particles in 2+1 dimensional first order gravity using a triangulation to fix the connection and frame-field. The Hamiltonian is reduced to a boundary term which yields the total mass. The triangulation is dynamical with…
Let $n\ge2$ and $\Omega$ be a bounded Lipschitz domain in $\mathbb{R}^n$. In this article, the authors investigate global (weighted) estimates for the gradient of solutions to Robin boundary value problems of second order elliptic equations…
Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping…
We construct supersymmetric gauge theories on some curved manifolds with boundaries. Our examples include a part of three-sphere and a part of two-sphere. We concentrate on Dirichlet boundary conditions. For these theories on the manifolds…