1,721,043 research outputs found
On the Lagrangian and Hamiltonian formulation of a scalar free field theory at null infinity
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Hadamard States From Null Infinity
No full textFree field theories on a four dimensional, globally hyperbolic spacetime, whose dynamics is ruled by a Green hyperbolic partial differential operator, can be quantized following the algebraic approach. It consists of a two-step procedure: In the first part one identifies the observables of the underlying physical system collecting them in a *-algebra which encodes their relational and structural properties. In the second step one must identify a quantum state, that is a positive, normalized linear functional on the *-algebra out of which one recovers the interpretation proper of quantum mechanical theories via the so-called Gelfand-Naimark-Segal theorem. In between the plethora of possible states, only few of them are considered physically acceptable and they are all characterized by the so-called Hadamard condition, a constraint on the singular structure of the associated two-point function. Goal of this paper is to outline a construction scheme for these states which can be applied whenever the underlying background possesses a null (conformal) boundary. We discuss in particular the examples of a real, massless conformally coupled scalar field and of linearized gravity on a globally hyperbolic and asymptotically flat spacetime
Remarks on the Reeh-Schlieder property for higher spin free fields on curved spacetimes
No full text The existence of states enjoying a weak form of the Reeh–Schlieder property has been recently established on curved backgrounds and in the framework of locally covariant quantum field theory. Since only the example of a real scalar field has been discussed, we extend the analysis to the case of massive and massless free fields either of spin-½ or of spin-1. In the process, it is also shown that both the vector potential and the Proca field can be described as a locally covariant quantum field theory. </jats:p
Tunnelling processes for Hadamard states through a 2+1 dimensional black hole and Hawking radiation
No full textWe analyse the local behaviour of the two-point correlation function of a quantum state for a scalar field in a neighbourhood of a Killing horizon in a 2+1-dimensional spacetime, extending the work of Moretti and Pinamonti in a 3+1-dimensional scenario. In particular we show that, if the state is of Hadamard form in such neighbourhood, similarly to the 3+1-dimensional case, under a suitable scaling limit towards the horizon, the two-point correlation function exhibits a thermal behaviour at the Hawking temperature. Since the whole analysis rests on the assumption that a Hadamard state exists in a neighbourhood of the Killing horizon, we show that this is not an empty condition by verifying it for a massive, real scalar field subject to Robin boundary conditions in the prototypic example of a three-dimensional black hole background: the non-extremal, rotating BTZ spacetime
Quantization of Maxwell's equations on curved backgrounds and general local covariance
No full textA quantization scheme for Maxwell’s equations without source is developed on an arbitrary oriented four-dimensional globally hyperbolic spacetime. The field strength tensor is the key dynamical object and it is not assumed a priori that it descends from a vector potential. It is shown that, in general, the associated field algebra can contain a non-trivial centre and, on account of this, such a theory cannot be described within the framework of general local covariance unless further restrictive assumptions on the topology of the spacetime are taken
Curvature fluctuations on asymptotically de Sitter spacetimes via the semiclassical Einsteinʼs equations
No full textt has been proposed recently to consider in the framework of cosmology an extension of the semiclassical Einsteinʼs equations in which the Einstein tensor is considered as a random function. This paradigm yields a hierarchy of equations between the n-point functions of the quantum, normal ordered, stress-energy tensor and those associated to the stochastic Einstein tensor. Assuming that the matter content is a conformally coupled massive scalar field on de Sitter spacetime, this framework has been applied to compute the power spectrum of the quantum fluctuations and to show that it is almost scale-invariant. We test the robustness and the range of applicability of this proposal by applying it to a less idealized, but physically motivated, scenario, namely we consider Friedmann–Robertson–Walker spacetimes which behave only asymptotically in the past as a de Sitter spacetime. We show in particular that, under this new assumption and independently from any renormalization freedom, the power spectrum associated to scalar perturbations of the metric behaves consistently with an almost scale-invariant power spectrum
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