The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes

Brunetti, Romeo; Fredenhagen, Klaus; Köhler, Michael

doi:10.1007/bf02099626

Cited by 218 publications

(485 citation statements)

References 24 publications

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“…For H 0 ∼ 10 16 GeV, the amplitude of the power spectrum is macroscopically large, and it provides an explanation of the observed temperature fluctuations in the cosmic microwave background as well as of "structure formation" in the universe, i.e., it produces density perturbations appropriate to act as "seeds" for the formation of clusters of galaxies and galaxies. The fact that, in the presence of exponential expansion, the short distance quantum fluctuations of fields in the very early universe can produce macroscopically observable effects in the present universe is one of the most remarkable predictions of QFTCS.…”

Section: D) Cosmological Perturbationsmentioning

confidence: 99%

“…However, there is a natural criterion to select physically reasonable states that is motivated from a variety of closely related considerations, including that (i) the ultra-high-frequency modes of the field should be essentially in their ground state, (ii) the short distance singular structure of the n-point functions W n should be similar to that of the n-point functions of the vacuum state in Minkowski spacetime, and (iii) the singular structure of the W n 's should be of "positive frequency type". A mathematically precise implementation of these requirements in a general curved spacetime can be formulated in the language of wave front sets discussed in Appendix A, as first proposed in [68,69] and [16]. The criterion is that the 2-point function have a wavefront set of the form…”

Section: Formulation Of Linear Qftcs Via the Algebraic Approach (Withmentioning

confidence: 99%

“…[32,34]. 16 Of course, the approximate description leading to this prediction should be valid only when M M P , where M P denotes the Planck mass (∼ 10 −5 gm), but modifications to the evaporation process at this stage (including the possibility of Planck mass remnants) would not significantly alter the discussion below. 17 This result, sometimes called "time-slice property", continues to hold for the enlarged algebra W defined in the next section and also for the algebra of interacting fields B I [26,55].…”

Section: C) Hawking Effectmentioning

confidence: 99%

“…The key breakthrough in this regard was made in [68,69]where the equivalence between (17) and (18) was proven-thereby enabling the methods of micolocal analysis to be applied to the renormalization problem, as first done in [16,17].…”

Section: Construction Of Nonlinear Observables For a Free Quantum Scamentioning

confidence: 99%

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Quantum fields in curved spacetime

2015

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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%