The Reeh–Schlieder Property for Quantum Fields on Stationary Spacetimes

Strohmaier, Alexander

doi:10.1007/s002200000299

Cited by 39 publications

(47 citation statements)

References 33 publications

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“…For spacetimes which are not analytic, a result by Strohmaier [19], extending an earlier result by Verch [21], shows that in a stationary spacetime all ground and thermal (KMS-)states of several types of free fields (including the Klein-Gordon, Dirac and Proca field) also have the Reeh-Schlieder property. To prove the existence of such states directly one may need to make further assumptions, depending on the type of field (see [19]). Furthermore, the condition of [20] can be weakened to a smoothly covariant condition that implies the Reeh-Schlieder property as well as physical relevance (i.e.…”

Section: Introductionsupporting

confidence: 54%

“…Now we can find an ultrastatic (and hence stationary) spacetime M diffeomorphic to M. Because m > 0 we may apply the results of [13], which imply the existence of a regular quasi-free ground state ω on M . This state has the Reeh-Schlieder property (see [19]) and is Hadamard because it satisfies the microlocal spectrum condition (see [15,20]). The conclusions now follow immediately from Theorem 4.1 and Corollaries 4.2 and 4.4.…”

Section: The Free Scalar Fieldmentioning

confidence: 99%

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On the Reeh-Schlieder Property in Curved Spacetime

Sanders

2009

Commun. Math. Phys.

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Abstract:We attempt to prove the existence of Reeh-Schlieder states on curved spacetimes in the framework of locally covariant quantum field theory using the idea of spacetime deformation and assuming the existence of a Reeh-Schlieder state on a diffeomorphic (but not isometric) spacetime. We find that physically interesting states with a weak form of the Reeh-Schlieder property always exist and indicate their usefulness. Algebraic states satisfying the full Reeh-Schlieder property also exist, but are not guaranteed to be of physical interest.

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Section: Introductionsupporting

confidence: 54%

Section: The Free Scalar Fieldmentioning

confidence: 99%

On the Reeh-Schlieder Property in Curved Spacetime

Sanders

2009

Commun. Math. Phys.

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“…One could work with Dirac spinors as well; then one has to introduce appropriate 'doublings' of spinor bundle and Dirac operator. Such an approach has, in the context of quantizing Dirac fields, been favoured elsewhere [11,21,27,29,35]. By employing somewhat more elaborate notation, one may generalize our results in Chapter 5 to the slightly more general case of Dirac spinors.…”

Section: Spin Structures and Spinor Fieldsmentioning

confidence: 90%

Microlocal Spectrum Condition and Hadamard Form for Vector-Valued Quantum Fields in Curved Spacetime

2001

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Abstract.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 set of their two-point functions (termed 'wavefront set spectrum condition'), thereby initiating a major progress in the understanding of Hadamard states and the further development of quantum field theory in curved spacetime. In the present work, we extend this important result on the equivalence of the wavefront set spectrum condition with the Hadamard condition from scalar fields to vector fields (sections in a vector bundle) which are subject to a wave-equation and are quantized so as to fulfill the covariant canonical commutation relations, or which obey a Dirac equation and are quantized according to the covariant anti-commutation relations, in any globally hyperbolic spacetime having dimension three or higher.In proving this result, a gap which is present in the published proof for the scalar field case will be removed. Moreover we determine the short-distance scaling limits of Hadamard states for vector-bundle valued fields, finding them to coincide with the corresponding flat-space, massless vacuum states.

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“…The generic occurrence of the Reeh-Schlieder property for large sets of physical states in quantum field theory -as so far known in quantum field theory on manifolds possessing suitable groups of isometries [38,44,13,16,29,46,39,12] -is a mathematically precise way of expressing that long-range correlations are a fundamental feature of quantum field theory. Furthermore, the Reeh-Schlieder property plays a very important role in analyzing the mathematical structure of quantum field theory.…”

Section: Introductionmentioning

confidence: 99%

Microlocal analysis of quantum fields on curved space–times: Analytic wave front sets and Reeh–Schlieder theorems

Strohmaier

Verch

Wollenberg

2002

Journal of Mathematical Physics

Self Cite

116

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We show in this article that the Reeh-Schlieder property holds for states of quantum fields on real analytic curved spacetimes if they satisfy an analytic microlocal spectrum condition. This result holds in the setting of general quantum field theory, i.e. without assuming the quantum field to obey a specific equation of motion. Moreover, quasifree states of the Klein-Gordon field are further investigated in the present work and the (analytic) microlocal spectrum condition is shown to be equivalent to simpler conditions. We also prove that any quasifree ground-or KMS-state of the Klein-Gordon field on a stationary real analytic spacetime fulfills the analytic microlocal spectrum condition.

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The Reeh–Schlieder Property for Quantum Fields on Stationary Spacetimes

Abstract: We prove the Reeh-Schlieder property for the ground-and KMSstates states of the massive Dirac Quantum field on a static globally hyperbolic 4 dimensional spacetime.

Cited by 39 publications

References 33 publications

On the Reeh-Schlieder Property in Curved Spacetime

On the Reeh-Schlieder Property in Curved Spacetime

Microlocal Spectrum Condition and Hadamard Form for Vector-Valued Quantum Fields in Curved Spacetime

Microlocal analysis of quantum fields on curved space–times: Analytic wave front sets and Reeh–Schlieder theorems

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