QED trace anomaly, non-local Lagrangians and quantum equivalence principle violations

Donoghue, John F.; El-Menoufi, Basem Kamal

doi:10.1007/jhep05(2015)118

Cited by 31 publications

(47 citation statements)

References 33 publications

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“…In §3 we apply this method to compute the effective action for the Yang-Mills field coupled to massless matter and for a self-interacting massless scalar field. In §3.5, we discuss the relation of our results to the nonlocal covariant perturbation theory developed by Barvinsky-Vilkovisky and similar results obtained by Donoghue and El-Menoufi [32,33] using Feynman diagrams in the weak field limit.…”

Section: Introductionsupporting

confidence: 62%

“…The form factors f and F as functions of the covariant Laplacian are generically non-local operators, and are to be understood as properly convoluted with the functions they act upon [4]. A similar result has been obtained for massless quantum electrodynamics by a somewhat different method by Donoghue and El-Menoufi [32,33] by evaluating the one-loop Feynman diagrams for small metric fluctuations around flat space and then covariantizing the answers.…”

Section: Barvinsky-vilkovisky Expansion and Conformal Decompositionmentioning

confidence: 64%

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Nonlocal quantum effective actions in Weyl-Flat spacetimes

Bautista

Dabholkar

2018

J. High Energ. Phys.

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Virtual massless particles in quantum loops lead to nonlocal effects which can have interesting consequences, for example, for primordial magnetogenesis in cosmology or for computing finite N corrections in holography. We describe how the quantum effective actions summarizing these effects can be computed efficiently for Weyl-flat metrics by integrating the Weyl anomaly or, equivalently, the local renormalization group equation. This method relies only on the local Schwinger-DeWitt expansion of the heat kernel and allows for a re-summation of leading large logarithms in situations where the Weyl factor changes by several e-foldings. As an illustration, we obtain the quantum effective action for the Yang-Mills field coupled to massless matter, and the self-interacting massless scalar field. Our action reduces to the nonlocal action obtained using the Barvinsky-Vilkovisky covariant perturbation theory in the regime R 2 ∇ 2 R for a typical curvature scale R, but has a greater range of validity effectively re-summing the covariant perturbation theory to all orders in curvatures. In particular, it is applicable also in the opposite regime R 2 ∇ 2 R, which is often of interest in cosmology.

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Section: Introductionsupporting

confidence: 62%

Section: Barvinsky-vilkovisky Expansion and Conformal Decompositionmentioning

confidence: 64%

Nonlocal quantum effective actions in Weyl-Flat spacetimes

Bautista

Dabholkar

2018

J. High Energ. Phys.

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“…The effective action in this expansion has been worked out to third order in curvatures [14][15][16][17]. Similar results have been obtained independently by Donoghue and El-Menoufi [18,19] using Feynman diagrams. Some of the earlier works on primordial magnetogenesis from anomalies, e.g.…”

Section: Introductionsupporting

confidence: 54%

To B or not to B: primordial magnetic fields from Weyl anomaly

Dabholkar

Kobayashi

2018

J. High Energ. Phys.

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The quantum effective action for the electromagnetic field in an expanding universe has an anomalous dependence on the scale factor of the metric arising from virtual charged particles in the loops. It has been argued that this Weyl anomaly of quantum electrodynamics sources cosmological magnetic fields in the early universe. We examine this long-standing claim by using the effective action beyond the weak gravitational field limit which has recently been determined. We introduce a general criteria for assessing the quantumness of field fluctuations, and show that the Weyl anomaly is not able to convert vacuum fluctuations of the gauge field into classical fluctuations. We conclude that there is no production of coherent magnetic fields in the universe from the Weyl anomaly of quantum electrodynamics, irrespective of the number of massless charged particles in the theory. arXiv:1808.08237v2 [hep-th]

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“…The associated expansion in curvature of this result can be relatively complicated. Indeed, one of us has calculated the full one-loop diagram for the photon propagator [44,45]. Such considerations can be carried out for Lee-Wick type theories, but that would take us a bit far from the scope of the present work.…”

Section: Stability and Energy Flowmentioning

confidence: 99%

Unitarity, stability, and loops of unstable ghosts

2019

Self Cite

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We present a new understanding of the unstable ghost-like resonance which appears in theories such as quadratic gravity and Lee-Wick type theories. Quantum corrections make this resonance unstable, such that it does not appear in the asymptotic spectrum. We prove that these theories are unitary to all orders. Unitarity is satisfied by the inclusion of only cuts from stable states in the unitarity sum. This removes the need to consider this as a ghost state in the unitarity sum. However, we often use a narrow-width approximation where we do include cuts through unstable states, and ignore cuts through the stable decay products. If we do this with the unstable ghost resonance at one loop, we get the correct answer only by using a contour which was originally defined by Lee and Wick. The quantum effects also provide damping in both the Feynman and the retarded propagators, leading to stability under perturbations. * Electronic address: donoghue@physics.umass.edu † Electronic address: gabrielmenezes@ufrrj.br arXiv:1908.02416v2 [hep-th] 21 Aug 2019 1.1. Unitarity with normal resonances Unitarity describes the conservation of probability for the S-matrix. It stateswhere we used the definition of the transfer matrix T , namely S = 1 + iT . Here the associated states are the asymptotic single and multiparticle states of the theory. In processes that involve loop diagrams, the sum over real intermediate states can by accomplished by the Cutkosky cutting rules [30] which project out the on-shell states. Procedurally we often look first at the free field theory to identify the free particles. Then when we include interactions, some of these particles become unstable and no longer appear as the asymptotic states of the theory. As far as the S-matrix is concerned, this is a significant change. The particles were originally needed in the Hilbert space for completeness, but then are no longer present in the interacting theory. The question then arises of how to treat such unstable particles in unitarity relations. Should one include them in the sums over states required for unitarity?The answer was provided by Veltman in 1963 [31], see also [32][33][34][35]. He showed that unitarity is indeed satisfied by the inclusion of only the asymptotically stable states. Cuts are not to be taken through the unstable particles, and unstable particles are not to be included in unitarity sums.However, there is a corollary which is useful in practice. In the narrow-width approximation, where the coupling to the decay products is taken to be very small, the off-resonance production becomes small and only resonance production is important. As we demonstrate in Sec. 6, in this limit a cut taken through the unstable particle with its width set to zero reproduces the same result as a cut through the decay products.This combination reinforces our intuition. The full calculation only requires the stable states, as unitarity demands. But when particles are nearly stable, we may approximate them as being stable in practical calculations. Unstable ghos...

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QED trace anomaly, non-local Lagrangians and quantum equivalence principle violations

Cited by 31 publications

References 33 publications

Nonlocal quantum effective actions in Weyl-Flat spacetimes

Nonlocal quantum effective actions in Weyl-Flat spacetimes

To B or not to B: primordial magnetic fields from Weyl anomaly

Unitarity, stability, and loops of unstable ghosts

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