Quantization of Linearized Gravity in Cosmological Vacuum Spacetimes

Fewster, Christopher J.; Hunt, David S.

doi:10.1142/s0129055x13300033

Cited by 54 publications

(124 citation statements)

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“…The classical advanced and retarded are well defined when smeared with test fields satisfying (126), and this is all that is needed to construct the analog of A for linearized gravity; for details see [31]. Consequently, all of the constructions and analyses given in section 2 for the free scalar field can be repeated, in parallel, for the linearized gravitational field, including the Hawking effect and the behavior of cosmological perturbations 28 .…”

Section: Quantum Gravitymentioning

confidence: 99%

Quantum Fields in Curved Spacetime

Hollands¹,

Wald²

2015

General Relativity and Gravitation

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We review the theory of quantum fields propagating in an arbitrary, classical, globally hyperbolic spacetime. Our review emphasizes the conceptual issues arising in the formulation of the theory and presents known results in a mathematically precise way. Particular attention is paid to the distributional nature of quantum fields, to their local and covariant character, and to microlocal spectrum conditions satisfied by physically reasonable states. We review the Unruh and Hawking effects for free fields, as well as the behavior of free fields in deSitter spacetime and FLRW spacetimes with an exponential phase of expansion. We review how nonlinear observables of a free field, such as the stress-energy tensor, are defined, as well as timeordered-products. The "renormalization ambiguities" involved in the definition of time-ordered products are fully characterized. Interacting fields are then perturbatively constructed. Our main focus is on the theory of a scalar field, but a brief discussion of gauge fields is included. We conclude with a brief discussion of a possible approach towards a nonperturbative formulation of quantum field theory in curved spacetime and some remarks on the formulation of quantum gravity. Quantum field theory in curved spacetime (QFTCS) is the theory of quantum fields propagating in a background, classical, curved spacetime (M , g). On account of its classical treatment of the metric, QFTCS cannot be a fundamental theory of nature. However, QFTCS is expected to provide an accurate description of quantum phenomena in a regime where the effects of curved spacetime may be significant, but effects of quantum gravity itself may be neglected. In particular, it is expected that QFTCS should be applicable to the description of quantum phenomena occurring in the early universe and near (and inside of) black holesprovided that one does not attempt to describe phenomena occurring so near to singularities that curvatures reach Planckian scales and the quantum nature of the spacetime metric would have to be taken into account.It should be possible to derive QFTCS by taking a suitable limit of a more fundamental theory wherein the spacetime metric is treated in accord with the principles of quantum theory. However, this has not been done-except in formal and/or heuristic ways-simply because no present quantum theory of gravity has been developed to the point where such a well defined limit can be taken. Rather, the framework of QFTCS that we shall describe in this review has been obtained by suitably merging basic principles of classical general relativity with the basic principles of quantum field theory in Minkowski spacetime. As we shall explain further below, the basic principles of classical general relativity are relatively easy to identify and adhere to, but it is far less clear what to identify as the "basic principles" of quantum field theory in Minkowski spacetime. Indeed, many of the concepts normally viewed as fundamental to quantum field theory in Minkowski spacetime, such as Poinca...

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Section: Quantum Gravitymentioning

confidence: 99%

Quantum Fields in Curved Spacetime

Hollands¹,

Wald²

2015

General Relativity and Gravitation

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“…This issue was discussed also in Refs. [141,142,143]. At the moment we are writing this review article, there is no consensus regarding this issue.…”

Section: Fixing the Residual Gauge Degrees Of Freedommentioning

confidence: 99%

Loops in inflationary correlation functions

Tanaka

Urakawa

2013

Class. Quantum Grav.

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Abstract. We review the recent progress regarding the loop corrections to the correlation functions in the inflationary universe. A naive perturbation theory predicts that loop corrections generated during inflation suffer from various infrared (IR) pathologies. Introducing an IR cutoff by hand is neither satisfactory nor enough to fix the problem of secular growth, which may ruin the predictive power of inflation models if the inflation lasts sufficiently long. We discuss the origin of the IR divergences and explore the regularity conditions of loop corrections for the adiabatic perturbation, the iso-curvature perturbation, and the tensor perturbation, in turn. These three kinds of perturbations have qualitative differences, but in discussing the IR regularity there is a feature common to all cases, which is the importance of the proper identification of observable quantities. Genuinely observable quantities should respect the gauge invariance from the view point of a local observer. Interestingly, we find that the requirement of the IR regularity restricts the allowed quantum states.

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“…The renormalisability of quantum Yang-Mills theories in curved spacetimes was established in [Hol08] and a general setting for linear quantised gauge field theories is given in [HS13]. One might also mention the progress made in linearised quantum gravity [FH13], which partly inspired some of the work just discussed. possess non-trivial centres.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Locality of the Free Maxwell Field

Fewster

Lang

2015

Ann. Henri Poincaré

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Abstract:We consider the non-interacting source-free Maxwell field, described both in terms of the vector potential and the field strength. Starting from the classical field theory on contractible globally hyperbolic spacetimes, we extend the classical field theory to general globally hyperbolic spacetimes in two ways to obtain a 'universal' theory and a 'reduced' theory. The quantum field theory in terms of the unital * -algebra of the smeared quantum field is then obtained by an application of a suitable quantisation functor. We show that the universal theories fail local covariance and dynamical locality owing to the possibility of having non-trivial radicals in the classical and non-trivial centres in the quantum case. The reduced theories are both locally covariant and dynamically local. These models provide new examples relevant to the discussion of how theories should be formulated so as to describe the same physics in all spacetimes.

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Quantization of Linearized Gravity in Cosmological Vacuum Spacetimes

Cited by 54 publications

References 50 publications

Quantum Fields in Curved Spacetime

Quantum Fields in Curved Spacetime

Loops in inflationary correlation functions

Dynamical Locality of the Free Maxwell Field

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