‘Vacuum-like’ Hadamard states for quantum fields on curved spacetimes

Brum, Marcos; Fredenhagen, Klaus

doi:10.1088/0264-9381/31/2/025024

Cited by 46 publications

(71 citation statements)

References 39 publications

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“…Yet, the ensuing state fails to obey to the Hadamard property as first observed in [13]. This seems to be a generic feature which can be cured only by introducing suitable ad-hoc cut-off functions as proposed in [6]. This is in sharp contrast with the behaviour of the FP state in space-times of infinite lifetime.…”

Section: Introductionmentioning

confidence: 95%

The fermionic signature operator in de Sitter spacetime

Dappiaggi

Finster

Murro

et al. 2020

Journal of Mathematical Analysis and Applications

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The fermionic projector state is a distinguished quasi-free state for the algebra of Dirac fields in a globally hyperbolic spacetime. We construct and analyze it in the four-dimensional de Sitter spacetime, both in the closed and in the flat slicing. In the latter case we show that the mass oscillation properties do not hold due to boundary effects. This is taken into account in a so-called mass decomposition. The involved fermionic signature operator defines a fermionic projector state. In the case of a closed slicing, we construct the fermionic signature operator and show that the ensuing state is maximally symmetric and of Hadamard form, thus coinciding with the counterpart for spinors of the Bunch-Davies state.

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Section: Introductionmentioning

confidence: 95%

The fermionic signature operator in de Sitter spacetime

Dappiaggi

Finster

Murro

et al. 2020

Journal of Mathematical Analysis and Applications

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“…Subsequently Sorkin (2011a) showed that the construction is also valid in the continuum, and can be used to give an alternative definition of the quantum field theory vacuum. This Sorkin-Johnston (SJ) vacuum provides a new insight into quantum field theory and has stimulated the interest of the algebraic field theory community (Fewster and Verch 2012;Brum and Fredenhagen 2014;Fewster 2018). The SJ vacuum has also been used to calculate Sorkin's spacetime entanglement entropy (SSEE) (Bombelli et al 1986;Sorkin 2014) in a causal set Sorkin and Yazdi 2018).…”

Section: Overviewmentioning

confidence: 99%

“…Since the SJ vacuum is intrinsically defined, at least in finite spacetime regions, one has a uniquely defined vacuum. As a result, the SJ state has generated some interest in the broader algebraic field theory community (Fewster and Verch 2012;Brum and Fredenhagen 2014;Fewster 2018). For example, while not in itself Hadamard in general, the SJ vacuum can be used to generate a new class of Hadamard states (Brum and Fredenhagen 2014).…”

Section: The Sorkin-johnston (Sj) Vacuummentioning

confidence: 99%

The causal set approach to quantum gravity

2019

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The causal set theory (CST) approach to quantum gravity postulates that at the most fundamental level, spacetime is discrete, with the spacetime continuum replaced by locally finite posets or "causal sets". The partial order on a causal set represents a proto-causality relation while local finiteness encodes an intrinsic discreteness. In the continuum approximation the former corresponds to the spacetime causality relation and the latter to a fundamental spacetime atomicity, so that finite volume regions in the continuum contain only a finite number of causal set elements. CST is deeply rooted in the Lorentzian character of spacetime, where a primary role is played by the causal structure poset. Importantly, the assumption of a fundamental discreteness in CST does not violate local Lorentz invariance in the continuum approximation. On the other hand, the combination of discreteness and Lorentz invariance gives rise to a characteristic non-locality which distinguishes CST from most other approaches to quantum gravity.In this review we give a broad, semi-pedagogical introduction to CST, highlighting key results as well as some of the key open questions. This review is intended both for the beginner student in quantum gravity as well as more seasoned researchers in the field.

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“…However, even if the PJ operator is itself 8 The use of the L 2 inner product for the SJ modes suggests the possibility that the SJ vacuum exists in a different sector of the theory. 9 Allen's theorem continues to hold in a finite region of spacetime as long as we choose this region to be symmetric about τ = 0, where τ is the time in hyperbolic coordinates (69). 10 In the causal set case we cannot take these temporal cutoffs to infinity, but we try to reach an asymptotic regime.…”

Section: The Massless De Sitter Sj Vacuummentioning

confidence: 99%

Studies on the SJ vacuum in de Sitter spacetime

Surya

Nomaan

Yazdi

2019

J. High Energ. Phys.

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In this work we study the Sorkin-Johnston (SJ) vacuum in de Sitter spacetime for free scalar field theory. For the massless theory we find that the SJ vacuum can neither be obtained from the O(4) Fock vacuum of Allen and Folacci nor from the non-Fock de Sitter invariant vacuum of Kirsten and Garriga. Using a causal set discretisation of a slab of 2d and 4d de Sitter spacetime, we find the causal set SJ vacuum for a range of masses m ≥ 0 of the free scalar field. While our simulations are limited to a finite volume slab of global de Sitter spacetime, they show good convergence as the volume is increased. We find that the 4d causal set SJ vacuum shows a significant departure from the continuum Mottola-Allen α-vacua. Moreover, the causal set SJ vacuum is well-defined for both the minimally coupled massless m = 0 and the conformally coupled massless m = m c cases. This is at odds with earlier work on the continuum de Sitter SJ vacuum where it was argued that the continuum SJ vacuum is ill-defined for these masses. Our results hint at an important tension between the discrete and continuum behaviour of the SJ vacuum in de Sitter and suggest that the former cannot in general be identified with the Mottola-Allen α-vacua even for m > 0.

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‘Vacuum-like’ Hadamard states for quantum fields on curved spacetimes

Cited by 46 publications

References 39 publications

The fermionic signature operator in de Sitter spacetime

The fermionic signature operator in de Sitter spacetime

The causal set approach to quantum gravity

Studies on the SJ vacuum in de Sitter spacetime

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