Passive states for essential observers

Strich, Robert

doi:10.1063/1.2838155

Cited by 5 publications

(8 citation statements)

References 23 publications

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“…• the thermodynamic behavior of the quantum systems It has also become clear through examples -quantum field theories on de Sitter space [10,25,44], anti-de Sitter space [24,30], a class of positively curved Robertson-Walker space-times [26,27], as well as others [92,98] -that the encoding of crucial physical information by modular objects and the subsequent utility of this approach are not limited to Minkowski space theories.…”

Section: Discussionmentioning

confidence: 99%

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Yet More Ado about Nothing: The Remarkable Relativistic Vacuum State

Summers¹

2011

Deep Beauty

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An overview is given of what mathematical physics can currently say about the vacuum state for relativistic quantum field theories on Minkowski space. Along with a review of classical results such as the Reeh-Schlieder Theorem and its immediate and controversial consequences, more recent results are discussed. These include the nature of vacuum correlations and the degree of entanglement of the vacuum, as well as the striking fact that the modular objects determined by the vacuum state and algebras of observables localized in certain regions of Minkowski space encode a remarkable range of physical information, from the dynamics and scattering behavior of the theory to the external symmetries and even the space-time itself. In addition, an intrinsic characterization of the vacuum state provided by modular objects is discussed. * This is an expanded version of an invited talk given at the Symposium "Deep Beauty: Mathematical Innovation and the Search for an Underlying Intelligibility of the Quantum World", held at Princeton University on October 3-4, 2007.

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Section: Discussionmentioning

confidence: 99%

“…After much effort, a number of interesting selection criteria have been isolated and studied; see, e.g. [10,16,24,25,29,30,43,61,66,71,78,92]. Of these, all but one either select an entire folium of statesi.e.…”

Section: Intrinsic Characterization Of the Vacuum Statementioning

confidence: 99%

Yet More Ado about Nothing: The Remarkable Relativistic Vacuum State

Summers¹

2011

Deep Beauty

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“…Besides the features we established above in the general admissible setting, the family of Minkowski wedges has the following well-known properties: wedges by taking property a) as their defining feature, see also the generalization by Strich [Str08]. In the de Sitter case, this definition is equivalent to our definition of a wedge as a connected component of the causal complement of an edge [BMS01].…”

Section: Definition 25 (Wedges)mentioning

confidence: 96%

Deformations of Quantum Field Theories on Spacetimes with Killing Vector Fields

Dappiaggi¹,

Lechner

Morfa-Morales³

2011

Commun. Math. Phys.

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The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedge-like regions which share the essential causal properties of the Poincaré transforms of the Rindler wedge in Minkowski space. In the setting of deformed quantum field theories, they play the role of typical localization regions of quantum fields and observables. As a concrete example of such a procedure, the deformation of the free Dirac field is studied.

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“…Starting points for the development of the proof of Theorem 3.1 were [BB99] for Part 1 and [Str08] for Part 2. Accordingly, we recover one of R. Strich's results as the following corollary.…”

Section: The Euler Element Theoremmentioning

confidence: 99%

Covariant Homogeneous Nets of Standard Subspaces

Morinelli

Neeb

2021

Commun. Math. Phys.

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Rindler wedges are fundamental localization regions in AQFT. They are determined by the one-parameter group of boost symmetries fixing the wedge. The algebraic canonical construction of the free field provided by Brunetti–Guido–Longo (BGL) arises from the wedge-boost identification, the BW property and the PCT Theorem. In this paper we generalize this picture in the following way. Firstly, given a $$\mathbb Z_2$$ Z 2 -graded Lie group we define a (twisted-)local poset of abstract wedge regions. We classify (semisimple) Lie algebras supporting abstract wedges and study special wedge configurations. This allows us to exhibit an analog of the Haag–Kastler one-particle net axioms for such general Lie groups without referring to any specific spacetime. This set of axioms supports a first quantization net obtained by generalizing the BGL construction. The construction is possible for a large family of Lie groups and provides several new models. We further comment on orthogonal wedges and extension of symmetries.

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Passive states for essential observers

Cited by 5 publications

References 23 publications

Yet More Ado about Nothing: The Remarkable Relativistic Vacuum State

Yet More Ado about Nothing: The Remarkable Relativistic Vacuum State

Deformations of Quantum Field Theories on Spacetimes with Killing Vector Fields

Covariant Homogeneous Nets of Standard Subspaces

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