The Extended Algebra of Observables for Dirac Fields and the Trace Anomaly of Their Stress-Energy Tensor

Dappiaggi, Claudio; Hack, Thomas-Paul; Pinamonti, Nicola

doi:10.1142/s0129055x09003864

Cited by 67 publications

(134 citation statements)

References 80 publications

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“…The two-point function, W 2 , of such a state may be described by a set of mode functions u k (t, x) = χ k (t) exp(ikx) as in eq. (24). Let us normalize the mode functions so that the Wronskian is i-times unity, i.e.,…”

Section: D) Cosmological Perturbationsmentioning

confidence: 99%

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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: D) Cosmological Perturbationsmentioning

confidence: 99%

“…In particular, analogs of W , B 0 , and B I can be defined for spinor fields in close parallel with the scalar case; see e.g. [24] for details.…”

Section: Yang-mills Fieldsmentioning

confidence: 99%

Quantum Fields in Curved Spacetime

Hollands¹,

Wald²

2015

General Relativity and Gravitation

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“…Although it turned out that this condition can not be fulfilled and that such unstable solutions can not be avoided, one can still analyse the subclass of stable solutions in a controlled manner in special cases, see e.g. [Sta80,Vil85,DFP08,Kok09,Pin10,DHMP10].…”

Section: (The Expectation Value Of)mentioning

confidence: 99%

On the stress–energy tensor of quantum fields in curved spacetimes—comparison of different regularization schemes and symmetry of the Hadamard/Seeley–DeWitt coefficients

Hack¹,

Moretti²

2012

J. Phys. A: Math. Theor.

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Abstract. We review a few rigorous and partly unpublished results on the regularisation of the stress-energy in quantum field theory on curved spacetimes: 1) the symmetry of the Hadamard/Seeley-DeWitt coefficients in smooth Riemannian and Lorentzian spacetimes 2) the equivalence of the local ζ-function and the Hadamard-point-splitting procedure in smooth static spacetimes 3) the equivalence of the DeWitt-Schwinger-and the Hadamard-point-splitting procedure in smooth Riemannian and Lorentzian spacetimes.

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“…Considering the global adS vacuum, we use the Hadamard method [4,5] to calculate the vacuum expectation value (v.e.v.) of the SET.…”

Section: Introductionmentioning

confidence: 99%

Dirac fermions on an anti-de Sitter background

Ambruş¹,

Winstanley²

2014

AIP Conference Proceedings

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Abstract. Using an exact expression for the bi-spinor of parallel transport, we construct the Feynman propagator for Dirac fermions in the vacuum state on anti-de Sitter space-time. We compute the vacuum expectation value of the stress-energy tensor by removing coincidence-limit divergences using the Hadamard method. We then use the vacuum Feynman propagator to compute thermal expectation values at finite temperature. We end with a discussion of rigidly rotating thermal states.

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The Extended Algebra of Observables for Dirac Fields and the Trace Anomaly of Their Stress-Energy Tensor

Cited by 67 publications

References 80 publications

Quantum Fields in Curved Spacetime

Quantum Fields in Curved Spacetime

On the stress–energy tensor of quantum fields in curved spacetimes—comparison of different regularization schemes and symmetry of the Hadamard/Seeley–DeWitt coefficients

Dirac fermions on an anti-de Sitter background

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