The Operator Product Expansion Converges in Perturbative Field Theory

Hollands, Stefan; Kopper, Christoph

doi:10.1007/s00220-012-1457-4

Cited by 34 publications

(95 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remarkably, for Euclidean perturbative φ 4 -theory, it has been shown that the series on the right side actually converges, at least at arbitrary but fixed order in perturbation theory [51,63]. If, as we expect, this also were found to be true at spacelike related points for theories on Lorentzian curved spacetimes, then this would strongly reinforce the view that the OPE coefficients contain the entire local information about the theory, even on a curved spacetime.…”

Section: Nonperturbative Formulation Of Interacting Qftcssupporting

confidence: 54%

Quantum fields in curved spacetime

2015

Self Cite

View full text Add to dashboard Cite

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...

show abstract

Section: Nonperturbative Formulation Of Interacting Qftcssupporting

confidence: 54%

Quantum fields in curved spacetime

2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…If the OPE is truncated by omitting terms with scaling dimension ∆ 0 and higher, the error decreases like A ∆ 0 /(∆ 0 !) 1/2 , where A depends on the state and is proportional to the separation [21].…”

Section: Truncation Of the Opementioning

confidence: 99%

Universal relation for the inelastic two-body loss rate

Braaten

Hammer

2013

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

Strongly-interacting systems consisting of particles that interact through a large scattering length satisfy universal relations that relate many of their central properties to the contact, which measures the number of pairs with small separations. We use the operator product expansion of quantum field theory to derive the universal relation for the inelastic 2-body loss rate. A simple universal relation between the loss rate and the contact is obtained by truncating the expansion after the lowest dimension operator. We verify the universal relation explicitly by direct calculations in the low-density limit at nonzero temperature. This universal relation can be tested experimentally using ultracold quantum gases of atoms in hyperfine states that have an inelastic spin-relaxation channel.

show abstract

“…The flow equation (4) gives us the running of O k appearing at the first order in ε. The term B k in (38) can be determined from equation (37). Let us note that if we set…”

Section: Conclusion and Outlooksmentioning

confidence: 99%

“…Equation (37) is potentially the starting point to study in a nonperturbative setting the correlation functions with two insertions of composite operators. In turn this implies the possibility of studying the operator product expansion coefficients along the lines of [34][35][36][37]. In this sense the study of the O (ε) terms is a first step in this direction.…”

Section: Conclusion and Outlooksmentioning

confidence: 99%

Note on scaling arguments in the effective average action formalism

Pagani

2016

Phys. Rev. D

View full text Add to dashboard Cite

The effective average action (EAA) is a scale dependent effective action where a scale k is introduced via an infrared regulator. The k−dependence of the EAA is governed by an exact flow equation to which one associates a boundary condition at a scale µ. We show that the µ−dependence of the EAA is controlled by an equation fully analogous to the Callan-Symanzik equation which allows to define scaling quantities straightforwardly. Particular attention is paid to composite operators which are introduced along with new sources. We discuss some simple solutions to the flow equation for composite operators and comment their implications in the case of a local potential approximation. arXiv:1603.07250v1 [hep-th]

show abstract

The Operator Product Expansion Converges in Perturbative Field Theory

Cited by 34 publications

References 17 publications

Quantum fields in curved spacetime

Quantum fields in curved spacetime

Universal relation for the inelastic two-body loss rate

Note on scaling arguments in the effective average action formalism

Contact Info

Product

Resources

About