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30
Axiomatic quantum field theory in curved spacetime
, 2008
"... The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincare invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globa ..."
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Cited by 689 (18 self)
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The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincare invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is locally and covariantly constructed from the spacetime metric), a microlocal spectrum condition, an "associativity" condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.
Modular localization and Wigner particles
- REV. MATH. PHYS
, 2002
"... We propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano-Wichmann relations and a representation of the Poincaré group on the one-particle Hilbert space. The abstract real Hilbert subspace version of the Tomita-Takesaki theory enab ..."
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Cited by 47 (8 self)
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We propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano-Wichmann relations and a representation of the Poincaré group on the one-particle Hilbert space. The abstract real Hilbert subspace version of the Tomita-Takesaki theory enables us to bypass some limitations of the Wigner formalism by introducing an intrinsic spacetime localization. Our approach works also for continuous spin representations to which we associate a net of von Neumann algebras on spacelike cones with the Reeh-Schlieder property. The positivity of the energy in the representation turns out to be equivalent to the isotony of the net, in the spirit of Borchers theorem. Our procedure extends to other spacetimes homogeneous under a group of geometric transformations as in the case of conformal symmetries and de Sitter spacetime.
Microlocal analysis of quantum fields on curved spacetimes: Analytic wavefront sets and Reeh-Schlieder theorems
, 2002
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Cosmological horizons and reconstruction of quantum field theories
, 2007
"... As a starting point for this manuscript, we remark how the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds shares some non trivial geometric properties with null infinity in an asymptotically flat spacetime. Such a feature is generalized to a larger class of expan ..."
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Cited by 24 (11 self)
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As a starting point for this manuscript, we remark how the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds shares some non trivial geometric properties with null infinity in an asymptotically flat spacetime. Such a feature is generalized to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon ℑ − common to all co-moving observers. This property is later exploited in order to recast, in a cosmological background, some recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable hypotheses on M – valid for deSitter spacetime and some other FRW spacetimes obtained by perturbing deSitter space – the algebra of observables for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables W(ℑ − ) constructed on the cosmological horizon. There is exactly one pure quasifree state λ on W(ℑ − ) which fulfils a suitable energypositivity condition with respect to a generator related with the cosmological time displacements. Furthermore λ induces a preferred physically meaningful quantum state λM for the quantum theory in the bulk. If M admits a timelike Killing generator preserving ℑ − , then the associated self-adjoint generator in the GNS representation of λM has positive spectrum (i.e. energy). Moreover λM turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of an expanding deSitter spacetime, λM coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity
Interacting Quantum Field Theory in de Sitter Vacua
, 2002
"... We discuss interacting quantum field theory in de Sitter space and argue that the Mottola-Allen vacuum ambiguity is an artifact of free field theory. The nature of the nonthermality of the MA-vacua is also clarified. We propose analyticity of correlation functions as a fundamental requirement of qua ..."
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Cited by 19 (0 self)
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We discuss interacting quantum field theory in de Sitter space and argue that the Mottola-Allen vacuum ambiguity is an artifact of free field theory. The nature of the nonthermality of the MA-vacua is also clarified. We propose analyticity of correlation functions as a fundamental requirement of quantum field theory in curved spacetimes. In de Sitter space, this principle determines the vacuum unambiguously and facilitates the systematic development of perturbation theory.
Particle decays and stability on the de Sitter universe
, 2008
"... We study particle decay in de Sitter space-time as given by first order perturbation theory in a Lagrangian interacting quantum field theory. We study in detail the adiabatic limit of the perturbative amplitude and compute the “phase space ” coefficient exactly in the case of two equal particles pro ..."
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Cited by 11 (3 self)
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We study particle decay in de Sitter space-time as given by first order perturbation theory in a Lagrangian interacting quantum field theory. We study in detail the adiabatic limit of the perturbative amplitude and compute the “phase space ” coefficient exactly in the case of two equal particles produced in the disintegration. We show that for fields with masses above a critical mass mc there is no such thing as particle stability, so that decays forbidden in flat space-time do occur here. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with mass lower than critical have a completely different behavior: the masses of their decay products must obey quantification rules, and their lifetime is zero. 1
An introduction to quantum field theory in de Sitter space-time
- in Cosmology and Gravitation: XIIth Brazilian School of Cosmology and Gravitation, AIP Conf. Proc
, 2007
"... We present a survey of rigourous quantization results obtained in recent works on quantum free fields in de Sitter space. For the “massive ” cases which are associated to principal series representations of the de Sitter group SO0(1, 4), the construction is based on analyticity requirements on the W ..."
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Cited by 7 (1 self)
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We present a survey of rigourous quantization results obtained in recent works on quantum free fields in de Sitter space. For the “massive ” cases which are associated to principal series representations of the de Sitter group SO0(1, 4), the construction is based on analyticity requirements on the Wightman two-point function. For the “massless ” cases (e.g. minimally coupled or conformal), associated to the discrete series, the quantization schemes are of the Gupta-Bleuler-Krein type. 1
Perturbative S-matrix for massive scalar fields in global de Sitter space
, 2014
"... We construct a perturbative S-matrix for interacting massive scalar fields in global de Sitter space. Our S-matrix is formulated in terms of asymptotic particle states in the far past and future, taking appropriate care for light fields whose wavefunctions decay only very slowly near the de Sitter c ..."
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Cited by 7 (1 self)
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We construct a perturbative S-matrix for interacting massive scalar fields in global de Sitter space. Our S-matrix is formulated in terms of asymptotic particle states in the far past and future, taking appropriate care for light fields whose wavefunctions decay only very slowly near the de Sitter conformal boundaries. An alternative for-mulation expresses this S-matrix in terms of residues of poles in analytically-continued Euclidean correlators (computed in perturbation theory), making it clear that the standard Minkowski-space result is obtained in the flat-space limit. Our S-matrix transforms properly under CPT, is invariant under the de Sitter isometries and pertur-bative field redefinitions, and is unitary. This unitarity implies a de Sitter version of the optical theorem. We explicitly verify these properties to second order in the cou-pling for a general cubic interaction, including both tree- and loop-level contributions. Contrary to other statements in the literature, we find that a particle of any positive mass may decay at tree level to any number of particles, each of arbitrary positive masses. In particular, even very light fields (in the complementary series of de Sitter representations) are not protected from tree-level decays.
Time-dependent spacetimes in AdS/CFT: Bubble and black hole
, 2004
"... We extend the study of time-dependent backgrounds in the AdS/CFT correspondence by examining the relation between bulk and boundary for the smooth ‘bubble of nothing ’ solution and for the locally AdS black hole which has the same asymptotic geometry. These solutions are asymptotically locally AdS, ..."
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Cited by 6 (0 self)
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We extend the study of time-dependent backgrounds in the AdS/CFT correspondence by examining the relation between bulk and boundary for the smooth ‘bubble of nothing ’ solution and for the locally AdS black hole which has the same asymptotic geometry. These solutions are asymptotically locally AdS, with a conformal boundary conformal to de Sitter space cross a circle. We study the cosmological horizons and relate their thermodynamics in the bulk and boundary. We consider the α-vacuum ambiguity associated with the de Sitter space, and find that only the Euclidean vacuum is well-defined on the black hole solution. We argue that this selects the Euclidean vacuum as the preferred state in the dual strongly coupled CFT.
Modular theory for the von Neumann algebras of local quantum physics
"... Abstract. In the first part, the second quantization procedure and the free Bosonic scalar field will be introduced, and the axioms for quantum fields and nets of observable algebras will be discussed. The second part is mainly devoted to an illustration of the BisognanoWichmann theorem for Wightma ..."
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Cited by 6 (0 self)
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Abstract. In the first part, the second quantization procedure and the free Bosonic scalar field will be introduced, and the axioms for quantum fields and nets of observable algebras will be discussed. The second part is mainly devoted to an illustration of the BisognanoWichmann theorem for Wightman fields and in the algebraic setting, with a discussion on the physical meaning of this result. In the third part some reconstruction theorems based on modular groups will be described, in particular the possibility of constructing an action of the symmetry group of a given theory via modular groups, and the construction of free field algebras via representations of the symmetry group.
