• Corpus ID: 237504151

Paracausal deformations of Lorentzian metrics and M{\o}ller isomorphisms in algebraic quantum field theory

@inproceedings{Moretti2021ParacausalDO,
  title={Paracausal deformations of Lorentzian metrics and M\{\o\}ller isomorphisms in algebraic quantum field theory},
  author={Valter Moretti and Simone Murro and Daniele Volpe},
  year={2021}
}
Given a pair of normally hyperbolic operators over (possibily different) globally hyperbolic spacetimes on a given smooth manifold, the existence of a geometric isomorphism, called Møller operator, between the space of solutions is studied. This is achieved by exploiting a new equivalence relation in the space of globally hyperbolic metrics, called paracausal relation. In particular, it is shown that the Møller operator associated to a pair of paracausally related metrics and normally… 

Figures from this paper

M{\o}ller operators and Hadamard states for Dirac fields with MIT boundary conditions
The aim of this paper is to prove the existence of Hadamard states for Dirac fields coupled with MIT boundary conditions on any globally hyperbolic manifold with timelike boundary. This is achieved
Globally hyperbolic spacetimes: slicings, boundaries and counterexamples
. The Cauchy slicings for globally hyperbolic spacetimes and their relation with the causal boundary are surveyed and revisited, starting at the seminal conformal boundary constructions by R.
Global and microlocal aspects of Dirac operators: propagators and Hadamard states
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

References

SHOWING 1-10 OF 64 REFERENCES
Hadamard States for the Klein–Gordon Equation on Lorentzian Manifolds of Bounded Geometry
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 spacetime
M{\o}ller operators and Hadamard states for Dirac fields with MIT boundary conditions
The aim of this paper is to prove the existence of Hadamard states for Dirac fields coupled with MIT boundary conditions on any globally hyperbolic manifold with timelike boundary. This is achieved
Constructing Hadamard States via an Extended Møller Operator
We consider real scalar field theories, whose dynamics is ruled by normally hyperbolic operators differing only by a smooth potential V. By means of an extension of the standard definition of Møller
Hadamard States for Quantum Abelian Duality
Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a $$\hbox {C}^*$$C∗-algebra of observables, which encompasses the
A local-to-global singularity theorem for quantum field theory on curved space-time
We prove that if a reference two-point distribution of positive type on a time orientable curved space-time (CST) satisfies a certain condition on its wave front set (the “classPM,g condition”) and
Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property
In a recent paper, we proved that a large class of spacetimes, not necessarily homogeneous or isotropous and relevant at a cosmological level, possesses a preferred codimension 1 submanifold, i.e.,
The Casimir Effect from the Point of View of Algebraic Quantum Field Theory
We consider a region of Minkowski spacetime bounded either by one or by two parallel, infinitely extended plates orthogonal to a spatial direction and a real Klein-Gordon field satisfying Dirichlet
Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime
Some years ago, Radzikowski has found a characterization of Hadamard states for scalar quantum fields on a four-dimensional globally hyperbolic spacetime in terms of a specific form of the wavefront
Micro-local approach to the Hadamard condition in quantum field theory on curved space-time
For the two-point distribution of a quasi-free Klein-Gordon neutral scalar quantum field on an arbitrary four dimensional globally hyperbolic curved space-time we prove the equivalence of (1) the
Absolute Quantum Energy Inequalities in Curved Spacetime
Abstract.Quantum Energy Inequalities (QEIs) are results which limit the extent to which the smeared renormalized energy density of the quantum field can be negative, when averaged along a timelike
...
...