相关论文: Boundary Operators in Euclidean Quantum Gravity
Two sets of spatially diffeomorphism invariant operators are constructed in the loop representation formulation of quantum gravity. This is done by coupling general relativity to an anti- symmetric tensor gauge field and using that field to…
Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering…
We explore a background-independent theory of composite gravity. The vacuum expectation value of the composite metric satisfies Einstein's equations (with corrections) as a consistency condition, and selects the vacuum spacetime. A…
Gravitational waves are considered as metric perturbations about a curved background metric, rather than the flat Minkowski metric since several situations of physical interest can be discussed by this generalization. In this case, when the…
Recent developments have made possible the computation of equilibrium dynamical correlators in quantum impurity problems. In many situations however, one is rather interested in correlators subject to a non equilibrium initial preparation;…
The unitary gauge fixing technique is applied to the QCD hamiltonian formulated in terms of angular variables. It is demonstrated that in this formulation projections on the physical Hilbert space are unnecessary to separate physical and…
Consider the Laplacian in a bounded domain in R^d with general (mixed) homogeneous boundary conditions. We prove that its eigenfunctions are `quasi-orthogonal' on the boundary with respect to a certain norm. Boundary orthogonality is proved…
Whereas local field operators play the crucial role in reconciling quantum mechanics and special relativity, they are not trivially compatible with the diffeomorphism invariance of gravity. In order to address this issue, we consider the…
We study the spectral behavior of higher order elliptic operators upon domain perturbation. We prove general spectral stability results for Dirichlet, Neumann and intermediate boundary conditions. Moreover, we consider the case of the…
In this paper, I investigate the quantisation of length in euclidean quantum gravity in three dimensions. The starting point is the classical hamiltonian formalism in a cylinder of finite radius. At this finite boundary, a counter term is…
In this work we obtain positive bounded solutions of various perturbations of \begin{equation} \left\{ \begin{array}{lcl} \hfill -\Delta u - \gamma \sum_{i,j=1}^N \frac{x_i x_j}{|x|^2} u_{x_i x_j} &=& u^p \qquad \mbox{ in } B_1, \\ \hfill u…
We show that the eigenvalues of the intrinsic Dirac operator on the boundary of a Euclidean domain can be obtained as the limits of eigenvalues of Euclidean Dirac operators, either in the domain with a MIT-bag type boundary condition or in…
We revisit the Extended Uncertainty Principle (EUP) from an operational viewpoint, replacing wavefunction-based widths with apparatus-defined position constraints such as a finite slit of width $\Delta x$ or a geodesic ball of radius $R$.…
The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the…
In this paper, we study eigenvalue of linear fourth order elliptic operators in divergence form with Dirichlet boundary condition on a bounded domain in a compact Riemannian manifolds with boundary (possibly empty) and find a general…
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of Euclidean space $\mR^{m+1}$ was recently constructed, including a higher dimensional analogue of the logarithmic function in the…
An alternative representation of the kernel of the evolution operator in quantum electrodynamics is obtained in the form of a functional integral, in which the gauge momentum corresponding to the Gaussian constraint is excluded from the…
Nonlocal boundary value problems with Dirichlet or Neumann boundary are well-studied for nonlocal operators of the type $\mathcal{L}_\gamma u = \operatorname{PV} \int_{\mathbb{R}^d} \big(u(\cdot)-u(y)\big) \gamma(\cdot,y) \, \mathrm{d}y$…
We consider the Dirichlet to Neumann operator for abelian Yang- Mills boundary conditions. We treat the case for space-time manifolds with general smooth boundary components. The aim is constructing a complex structure for the symplectic…
Quantum mechanical boundary conditions along a timelike line, corresponding to the origin in radial coordinates, in two-dimensional dilaton gravity coupled to $N$ matter fields, are considered. Conformal invariance and vacuum stability…