A new class of Fermionic Projectors: Møller operators and mass oscillation properties

Drago, Nicolò; Murro, Simone

doi:10.1007/s11005-017-0998-z

Cited by 15 publications

(12 citation statements)

References 56 publications

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“…non-perturbative, *isomorphism R cl λQ{χµ} : A λQ{χµ} → A between the algebra A λQ{χµ} of quantum observables associated to the free Klein-Gordon field whose dynamics is ruled by the operator + m 2 + λm 2 0 χ µ and the algebra A. Its pull-back action on states has been studied in [20,29] and will be exploited in the following -cf. equation (20).…”

Section: Quantum Møller Operatormentioning

confidence: 99%

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Thermal State with Quadratic Interaction

Drago

2018

Ann. Henri Poincaré

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We consider the perturbative construction, proposed in [37], for a thermal state Ω β,λV {f } for the theory of a real scalar Klein-Gordon field φ with interacting potential V {f }. Here f is a spacetime cut-off of the interaction V and λ is a perturbative parameter. We assume that V is quadratic in the field φ and we compute the adiabatic limit f → 1 of the state Ω β,λV {f } . The limit is shown to exist, moreover, the perturbative series in λ sums up to the thermal state for the corresponding (free) theory with potential V . In addition, we exploit the same methods to address a similar computation for the non-equilibrium steady state (NESS) [59] recently constructed in [25].

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Section: Quantum Møller Operatormentioning

confidence: 99%

“…From equation (29) it follows that the coefficients c n,k coincide with the Eulerian numbers A(n, k) [10, Thm. 1.7], that is, c n,k is the number of n-permutations with k − 1 descents.…”

Section: β-Expansion Of the Bose-einstein Factormentioning

confidence: 99%

Thermal State with Quadratic Interaction

Drago

2018

Ann. Henri Poincaré

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“…It was introduced in [19,20] and it has the advantage of producing a distinguished quasi-free, pure state for the C * -algebra of Dirac quantum fields, provided that a suitable condition, known as the strong mass oscillation property, holds true [17]. For a related analysis, containing a weaker but non-canonical condition, refer to [11]. The advantage of focusing on the FP state is that it does not rely on the existence of any specific Killing isometry and thus it can be applied in a large class of scenarios.…”

Section: Introductionmentioning

confidence: 99%

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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“…Amongst numerous other nice properties, they ensure that quantum fluctuations of observables are bounded and allow for an extension of the algebra of fields to encompass Wick polynomials [32][33][34][35][36][37][38][39]. Over the years, the notion of Hadamard states has proved successful in a wide range of different settings, see, e.g., [40][41][42][43][44][45][46][47][48][49][50][51][52][53], to name a few.…”

Section: Definition 4 (Quasifree State) a Statementioning

confidence: 99%

Partial Differential Equations and Quantum States in Curved Spacetimes

Avetisyan

Capoferri

2021

Mathematics

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In this review paper, we discuss the relation between recent advances in the theory of partial differential equations and their applications to quantum field theory on curved spacetimes. In particular, we focus on hyperbolic propagators and the role they play in the construction of physically admissible quantum states—the so-called Hadamard states—on globally hyperbolic spacetimes. We will review the notion of a propagator and discuss how it can be constructed in an explicit and invariant fashion, first on a Riemannian manifold and then on a Lorentzian spacetime. Finally, we will recall the notion of Hadamard state and relate the latter to hyperbolic propagators via the wavefront set, a subset of the cotangent bundle capturing the information about the singularities of a distribution.

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A new class of Fermionic Projectors: Møller operators and mass oscillation properties

Cited by 15 publications

References 56 publications

Thermal State with Quadratic Interaction

Thermal State with Quadratic Interaction

The fermionic signature operator in de Sitter spacetime

Partial Differential Equations and Quantum States in Curved Spacetimes

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