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Register a new userVilkovisky unique effective action in quantum gravity
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The divergent part of the one-loop Vilkovisky unique effective action for quantum Einstein gravity is evaluated in the general parametrization of the quantum field, including the separated conformal factor. The output of this calculation explicitly demonstrates the parametrization and conformal gauge independence of the unique effective action with the configuration space metric chosen following Vilkoviskys prescription.
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The effective action in quantum general relativity is strongly dependent on the gauge-fixing and parametrization of the quantum metric. As a consequence, in the effective approach to quantum gravity, there is no possibility to introduce the renormalization-group framework in a consistent way. On the other hand, the version of effective action proposed by Vilkovisky and DeWitt does not depend on the gauge-fixing and parametrization off-shell, opening the way to explore the running of the cosmological and Newton constants as well as the coefficients of the higher-derivative terms of the total action. We argue that in the effective framework the one-loop beta functions for the zero-, two- and four-derivative terms can be regarded as exact, that means, free from corrections coming from the higher loops. In this perspective, the running describes the renormalization group flow between the present-day Hubble scale in the IR and the Planck scale in the UV.
We compute the classical effective action of color charges moving along worldlines by integrating out the Yang-Mills gauge field to next-to-leading order in the coupling. An adapted version of the Bern-Carrasco-Johansson (BCJ) double-copy construction known from quantum scattering amplitudes is then applied to the Feynman integrands, yielding the prediction for the classical effective action of point masses in dilaton gravity. We check the validity of the result by independently constructing the effective action in dilaton gravity employing field redefinitions and gauge choices that greatly simplify the perturbative construction. Complete agreement is found at next-to-leading order. Finally, upon performing the post-Newtonian expansion of our result, we find agreement with the corresponding action of scalar-tensor theories known from the literature. Our results represent a proof of concept for the classical double-copy construction of the gravitational effective action and provides another application of a BCJ-like double copy beyond scattering amplitudes.
We demonstrate that a recently proposed classical double copy procedure to construct the effective action of two massive particles in dilaton-gravity from the analogous problem of two color charged particles in Yang-Mills gauge theory fails at next-to-next-to-leading orders in the post-Minkowskian (3PM) or post-Newtonian (2PN) expansions.
The quantum effective action yields equations of motion and correlation functions including all quantum corrections. We discuss here how it encodes also Noether currents at the full quantum level. This holds both for covariantly conserved currents associated to real symmetries that leave the action invariant as well as for non-conserved Noether currents associated to extended symmetry transformations which change the action, but in a specific way. We discuss then in particular symmetries and extended symmetries associated to space-time geometry for relativistic quantum field theories. These encompass local dilatations or Weyl gauge transformation, local Lorentz transformations and local shear transformations. Together they constitute the symmetry group of the frame bundle GL$(d)$. The corresponding non-conserved Noether currents are the dilatation or Weyl current, the spin current and the shear current for which divergence-type equations of motion are obtained from the quantum effective action.
Spontaneous pair production from background fields or spacetimes is one of the most prominent phenomena predicted by quantum field theory. The Schwinger mechanism of production of charged pairs by a strong electric field and the Hawking radiation of all species of particles from a black hole are the consequence of nonperturbative quantum effects. In this review article, the vacuum structure and pair production is reviewed in the in-out formalism, which provides a consistent framework for quantum field theory in the sense that the complex action explains not only the vacuum persistence but also pair production. The current technology of intense lasers is still lower by a few order than the Schwinger limit for electron-positron pair production, while magnetic fields of magnetars on the surface are higher than the Schwinger limit and even higher at the core. On the other hand, the zero effective mass of electron and hole in graphene and Dirac or Weyl semimetals will open a window for experimental test of quantum electrodynamics (QED) phenomena in strong fields.
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