Search results for "Normalization"
showing 10 items of 632 documents
Composite operators in asymptotic safety
2017
We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dim…
On the Possibility of Quantum Gravity Effects at Astrophysical Scales
2007
The nonperturbative renormalization group flow of Quantum Einstein Gravity (QEG) is reviewed. It is argued that at large distances there could be strong renormalization effects, including a scale dependence of Newton's constant, which mimic the presence of dark matter at galactic and cosmological scales.
ON QUANTUM GRAVITY, ASYMPTOTIC SAFETY AND PARAMAGNETIC DOMINANCE
2012
We discuss the conceptual ideas underlying the Asymptotic Safety approach to the nonperturbative renormalization of gravity. By now numerous functional renormalization group studies predict the existence of a suitable nontrivial ultraviolet fixed point. We use an analogy to elementary magnetic systems to uncover the physical mechanism behind the emergence of this fixed point. It is seen to result from the dominance of certain paramagnetic-type interactions over diamagnetic ones. Furthermore, the spacetimes of Quantum Einstein Gravity behave like a polarizable medium with a "paramagnetic" response to external perturbations. Similarities with the vacuum state of Yang-Mills theory are pointed …
Remarks on the renormalization of primordial cosmological perturbations
2011
We briefly review the need to perform renormalization of inflationary perturbations to properly work out the physical power spectra. We also summarize the basis of (momentum-space) renormalization in curved spacetime and address several misconceptions found in recent literature on this subject.
Spacetime correlators of perturbations in slow-roll de Sitter inflation
2014
Two-point correlators and self-correlators of primordial perturbations in quasi-de Sitter spacetime backgrounds are considered. For large separations two-point correlators exhibit nearly scale invariance, while for short distances self-correlators need standard renormalization. We study the deformation of two-point correlators to smoothly match the self-correlators at coincidence. The corresponding angular power spectrum is evaluated in the Sachs-Wolfe regime of low multipoles. Scale invariance is maintained, but the amplitude of $C_{\ell}$ could change in a non-trivial way.
Hopf algebras, renormalization and noncommutative geometry
1998
We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of transverse index theory for foliations.
Normalization of Killing vectors and energy conservation in two-dimensional gravity
1999
We explicitly show that, in the context of a recently proposed 2D dilaton gravity theory, energy conservation requires the ``natural'' Killing vector to have, asymptotically, an unusual normalization. The Hawking temperature $T_H$ is then calculated according to this prescription.
Conformal sector of quantum Einstein gravity in the local potential approximation: Non-Gaussian fixed point and a phase of unbroken diffeomorphism in…
2008
We explore the nonperturbative renormalization group flow of quantum Einstein gravity (QEG) on an infinite dimensional theory space. We consider ``conformally reduced'' gravity where only fluctuations of the conformal factor are quantized and employ the local potential approximation for its effective average action. The requirement of ``background independence'' in quantum gravity entails a partial differential equation governing the scale dependence of the potential for the conformal factor which differs significantly from that of a scalar matter field. In the infinite dimensional space of potential functions we find a Gaussian as well as a non-Gaussian fixed point which provides further e…
Adiabatic regularization and particle creation for spin one-half fields
2013
The extension of the adiabatic regularization method to spin-$1/2$ fields requires a self-consistent adiabatic expansion of the field modes. We provide here the details of such expansion, which differs from the WKB ansatz that works well for scalars, to firmly establish the generalization of the adiabatic renormalization scheme to spin-$1/2$ fields. We focus on the computation of particle production in de Sitter spacetime and obtain an analytic expression of the renormalized stress-energy tensor for Dirac fermions.
Cosmology with self-adjusting vacuum energy density from a renormalization group fixed point
2001
Cosmologies with a time dependent Newton constant and cosmological constant are investigated. The scale dependence of $G$ and $\Lambda$ is governed by a set of renormalization group equations which is coupled to Einstein's equation in a consistent way. The existence of an infrared attractive renormalization group fixed point is postulated, and the cosmological implications of this assumption are explored. It turns out that in the late Universe the vacuum energy density is automatically adjusted so as to equal precisely the matter energy density, and that the deceleration parameter approaches $q = -1/4$. This scenario might explain the data from recent observations of high redshift type Ia S…