A Distinguished Vacuum State for a Quantum Field in a Curved Spacetime: Formalism, Features, and Cosmology

Afshordi, Niayesh; Aslanbeigi, Siavash; Sorkin, Rafael D.

doi:10.48550/arxiv.1205.1296

Cited by 13 publications

(49 citation statements)

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“…Since, at this level, the metric behaves like a background field and hence we are neglecting any backreaction, ξR has the role of an effective point-dependent mass term. There is no a priori reason to believe that a certain value of ξ is preferred, though ξ = 0 and ξ = 1 6 are distinguished, the first representing the so-called minimal coupling and the second the conformal coupling. While the reason behind the choice of the word minimal is rather straightforward, the adjective conformal refers to a special property of (3.8).…”

Section: Scalar Fieldsmentioning

confidence: 99%

“…To wit, let us consider a globally hyperbolic spacetime (M, g) and a conformally rescaled one (M, g ′ ), namely, g ′ = Ω 2 g up to an isometry, where Ω is a smooth and strictly positive function on M . Then, to every solution Φ of (3.8) with m 2 = 0 and ξ = 1 6 on (M, g), one can build Φ ′ = Ω −1 Φ, which is a solution of the very same partial differential equation on (M, g ′ ).…”

Section: Scalar Fieldsmentioning

confidence: 99%

“…On a generic globally hyperbolic spacetime, the potential lack of a non-trivial isometry group forces us to follow a different approach. In a four dimensional Lorentzian manifold, the starting point is the spin group, 87 the double cover of SO (3,1). Its component connected to the identity is, therefore, isomorphic to SL(2, C).…”

Section: Majorana Fieldsmentioning

confidence: 99%

“…We denote the collection of all these frames at x as F x M . Since two elements of F x M can be always mapped into each other by the action of an element of the proper orthochronous Lorentz group, by fixing an element, we can identify F x M with the Lie group SO 0 (3,1). Since the tangent space of a globally hyperbolic spacetime M is trivial, that is T M ≃ M × R 4 , it turns out that F M , the disjoint union x∈M F x M , is isomorphic to M × SO 0 (3, 1) as a principal bundle.…”

Section: Majorana Fieldsmentioning

confidence: 99%

“…1. ρ preserves the fibers, that is to say that the image of S x M lies in F x M ; 2. ρ is equivariant, i.e., using Π to denote the surjective homomorphism from SL(2, C) to SO 0 (3,1), Notice that, as for F M , also SM , the spin bundle is defined using the language of principal bundles. Nonetheless, if M is globally hyperbolic, one can prove g that M admits only the trivial principal SL(2, C)bundle.…”

Section: Majorana Fieldsmentioning

confidence: 99%

See 4 more Smart Citations

Quantum Field Theory on Curved Backgrounds — A Primer

Benini

Dappiaggi

Hack

2013

Int. J. Mod. Phys. A

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Goal of this review is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, it is assigned to a physical system a suitable algebra of observables, which is meant to encode all algebraic relations among observables, such as commutation relations. In the second step, one must select an algebraic state in order to recover the standard Hilbert space interpretation of a quantum system. As quantum field theories possess infinitely many degrees of freedom, many unitarily inequivalent Hilbert space representations exist and the power of such approach is the ability to treat them all in a coherent manner. We will discuss in detail the algebraic approach for free fields in order to give to the reader all necessary information to deal with the recent literature, which focuses on the applications to specific problems, mostly in cosmology.Keywords: quantum field theory on curved backgrounds, algebraic quantum field theory PACS numbers: 04.62.+v, 11.10.Cd or lightlike vector depending whether its length g(v p , v p ) is smaller, greater or equal to 0 respectively. In this way, as in Minkowski spacetime, we divide T p M into two regions, the set of spacelike vectors, and the two-folded light cone stemming from 0, the origin of the vector space T p M . For each point p ∈ M we have the freedom to designate each of the folds of the light cone of T p M as the set of future-directed and of pastdirected vectors respectively. If we can smoothly specify at each point which one of the two cones is the future one, we say that (M, g) is time orientable. 123 This is equivalent to the existence of a global vector field on M which is timelike everywhere. Henceforth we will only consider pairs (M, g) enjoying this property and, moreover, we shall assume that a time orientation has been fixed. This allows to introduce J ± M even when (M, g) is not isometric to (R 4 , η). To be precise, in the first place one has to define timelike, lightlike and spacelike curves: A piecewise smooth curve γ : I → M , I ∈ [0, 1], is timelike (lightlike or spacelike) if, for every t ∈ I, the vector tangent to the curve at γ(t) is timelike (respectively lightlike or spacelike). A curve is called causal if it is nowhere spacelike. For causal curves, one can also specify the direction according to the time orientation of (M, g): A causal curve γ : I → M is future-(past-) directed if for each t ∈ I each vector tangent to γ at γ(t) lies in the future (respectively past) fold of T γ(t) M . Given these preliminaries, for any p ∈ M we call causal future of p the set J + M (p) of points q ∈ M which can be reached by a future-directed causal curve stemming from p. Replacing future-directed causal curves with past-directed ones, we define also the causal past of p, J − M (p). Notice that, if we allow only timelike (in place of causal) curves, we replace J ± M (p) with I ± M (p), namely the chronological future (+) an...

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Section: Scalar Fieldsmentioning

confidence: 99%

Section: Scalar Fieldsmentioning

confidence: 99%

Section: Majorana Fieldsmentioning

confidence: 99%

Section: Majorana Fieldsmentioning

confidence: 99%

Section: Majorana Fieldsmentioning

confidence: 99%

See 3 more Smart Citations

Quantum Field Theory on Curved Backgrounds — A Primer

Benini

Dappiaggi

Hack

2013

Int. J. Mod. Phys. A

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Hadamard States from Light-like Hypersurfaces

Dappiaggi

Moretti

Pinamonti

2017

SpringerBriefs in Mathematical Physics

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A preferred ground state for the scalar field in de Sitter space

Aslanbeigi

Buck

2013

J. High Energ. Phys.

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We investigate a recent proposal for a distinguished vacuum state of a free scalar quantum field in an arbitrarily curved spacetime, known as the Sorkin-Johnston (SJ) vacuum, by applying it to de Sitter space. We derive the associated two-point functions on both the global and Poincaré (cosmological) patches in general d + 1 dimensions. In all cases where it is defined, the SJ vacuum belongs to the family of de Sitter invariant α-vacua. We obtain different states depending on the spacetime dimension, mass of the scalar field, and whether the state is evaluated on the global or Poincaré patch. We find that the SJ vacuum agrees with the Euclidean/Bunch-Davies state for heavy ("principal series") fields on the global patch in even spacetime dimensions. We also compute the SJ vacuum on a causal set corresponding to a causal diamond in 1 + 1 dimensional de Sitter space. Our simulations show that the mean of the SJ two-point function on the causal set agrees well with its expected continuum counterpart.

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A Distinguished Vacuum State for a Quantum Field in a Curved Spacetime: Formalism, Features, and Cosmology

Cited by 13 publications

References 0 publications

Quantum Field Theory on Curved Backgrounds — A Primer

Quantum Field Theory on Curved Backgrounds — A Primer

Hadamard States from Light-like Hypersurfaces

A preferred ground state for the scalar field in de Sitter space

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