The art of the state

Fewster, Christopher J.

doi:10.1142/s0218271818430071

Cited by 16 publications

(18 citation statements)

References 57 publications

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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%

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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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Section: Overviewmentioning

confidence: 99%

Section: The Sorkin-johnston (Sj) Vacuummentioning

confidence: 99%

The causal set approach to quantum gravity

2019

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“…A remarkable fact is that the Hadamard condition (7), together with the algebraic relations in A (M), fixes the two-point function up to smooth terms (see [30,31] for reviews and original references). In particular, the difference of any two Hadamard two-point functions is smooth.…”

Section: Definitionmentioning

confidence: 99%

Quantum strong energy inequalities

Fewster

Kontou

2019

Phys. Rev. D

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Quantum energy inequalities (QEIs) express restrictions on the extent to which weighted averages of the renormalized energy density can take negative expectation values within a quantum field theory. Here we derive, for the first time, QEIs for the effective energy density (EED) for the quantized non-minimally coupled massive scalar field. The EED is the quantity required to be non-negative in the strong energy condition (SEC), which is used as a hypothesis of the Hawking singularity theorem. Thus establishing such quantum strong energy inequalities (QSEIs) is a first step towards a singularity theorem for matter described by quantum field theory.More specifically, we derive difference QSEIs, in which the local average of the EED is normalordered relative to a reference state, and averaging occurs over both timelike geodesics and spacetime volumes. The resulting QSEIs turn out to depend on the state of interest. We analyse the state-dependence of these bounds in Minkowski spacetime for thermal (KMS) states, and show that the lower bounds grow more slowly in magnitude than the EED itself as the temperature increases. The lower bounds are therefore of lower energetic order than the EED, and qualify as nontrivial state-dependent QEIs.

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“…Since it is impossible to choose a distinguished ("vacuum") state which is Hadamard consistently for an arbitrary spacetime [37,38], the first possibility involves an arbitrary choice for each spacetime. In contrast, the second possibility is uniquely defined for an arbitrary spacetime.…”

Section: )mentioning

confidence: 99%

Trace anomaly for chiral fermions via Hadamard subtraction

Fröb

Zahn

2019

J. High Energ. Phys.

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We calculate the trace (conformal) anomaly for chiral fermions in a general curved background using Hadamard subtraction. While in intermediate steps of the calculation imaginary terms proportional to the Pontryagin density appear, imposing a vanishing divergence of the stress tensor these terms completely cancel, and we recover the wellknown result equal to half the trace anomaly of a Dirac fermion. We elaborate in detail on the advantages of the Hadamard method for the general definition of composite operators in general curved spacetimes, and speculate on possible causes for the appearance of the Pontryagin density in other calculations.

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The art of the state

Cited by 16 publications

References 57 publications

The causal set approach to quantum gravity

The causal set approach to quantum gravity

Quantum strong energy inequalities

Trace anomaly for chiral fermions via Hadamard subtraction

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