相关论文: Analytic Hadamard states, Calder\'on projectors an…

We set up a general framework for Calder\'on projectors (and their generalization to non-compact manifolds), associated with complex Laplacians e.g. obtained by Wick rotation of a Lorentzian metric. In the analytic case, we use this to show…

We consider the Klein-Gordon equation on a class of Lorentzian manifolds with Cauchy surface of bounded geometry, which is shown to include examples such as exterior Kerr, Kerr-de Sitter and Kerr-Kruskal spacetimes. In this setup, we give…

Motivated by the quantization of linearized gravity, we consider gauge-fixed linearized Einstein equations and their Wick rotation near a Cauchy surface. We show that Calder\'on projectors for the Wick-rotated equations induce Hadamard…

We consider the massive Klein-Gordon equation on a class of asymptotically static spacetimes (in the long range sense) with Cauchy surface of bounded geometry. We prove the existence and Hadamard property of the in and out states…

We revisit the construction by Sanders [S1] of the Hartle-Hawking-Israel state for a free quantum Klein-Gordon field on a spacetime with a static, bifurcate Killing horizon and a wedge reflection. Using the notion of the Calder{\'o}n…

We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge--Dirac operator on…

We construct a class of solutions to the Cauchy problem of the Klein-Gordon equation on any standard static spacetime. Specifically, we have constructed solutions to the Cauchy problem based on any self-adjoint extension (satisfying a…

Hadamard states are generally considered as the physical states for linear quantized fields on curved spacetimes, for several good reasons. Here, we provide a new motivation for the Hadamard condition: for "ultrastatic slab spacetimes" with…

We consider the quantization of linearized Einstein equations. We prove the existence of Hadamard states in the harmonic gauge on any Einstein spacetime with compact Cauchy surfaces.

We propose a geometric approach to construct the Cauchy evolution operator for the Lorentzian Dirac operator on Cauchy-compact globally hyperbolic 4-manifolds. We realise the Cauchy evolution operator as the sum of two invariantly defined…

We show that the spatial part of the Klein-Gordon operator is an essentially self-adjoint operator on the Cauchy surfaces of various classes of spacetimes. Our proof employs the intricate connection between global hyperbolicity and…

We give an introduction to the techniques from microlocal analysis that have successfully been applied in the investigation of Hadamard states of free quantum field theories on curved spacetimes. The calculation of the wave front set of the…

We construct states on the algebra of the Klein-Gordon field that minimize the energy density in homogeneous and in inhomogeneous spacetimes, both with compact Cauchy hypersurfaces. The energy density is measured by geodesic observers and…

We consider the Klein-Gordon operator on an $n$-dimensional asymptotically anti-de Sitter spacetime $(M,g)$ together with arbitrary boundary conditions encoded by a self-adjoint pseudodifferential operator on $\partial M$ of order up to…

In this paper we propose a definition of quasifree Hadamard states for spinor fields on a curved space-time by specifying the Polarisation Set of the two-point function. We prove that the thermal equilibrium state on an ultrastatic…

High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of…

Quasifree states of a linear Klein-Gordon quantum field on globally hyperbolic spacetime manifolds are considered. Using techniques from the theory of pseudodifferential operators and wavefront sets on manifolds a criterion for a state to…

We construct Hadamard states for Klein-Gordon fields in a spacetime $M_{0}$ equal to the interior of the future lightcone $C$ from a base point $p$ in a globally hyperbolic spacetime $(M, g)$. Under some regularity conditions at future…

Developments in numerical methods for problems governed by nonlinear partial differential equations underpin simulations with sound arguments in diverse areas of science and engineering. In this paper, we explore the regularization method…

We study the inverse problem of determining the coefficients of the fractional power of a general second order elliptic operator given in the exterior of an open subset of the Euclidean space. We show the problem can be reduced into…