Search results for "Renormalization"
showing 10 items of 470 documents
Depletion in Bose-Einstein condensates using quantum field theory in curved space
2007
5 pages.-- PACS nrs.: 03.75.Kk; 05.30.Jp; 04.62.+v; 04.70.Dy.-- ISI Article Identifier: 000246074600122.-- ArXiv pre-print available at: http://arxiv.org/abs/cond-mat/0610367
Domains of Convergence of Kam Type Iterations for Eigenvalue Problems
1999
The KAM technique was first introduced to deal with small denominator problems appearing in perturbation of invariant tori in classical mechanics [1, 2]. Similar methods were later applied to many different problems, like e.g. eigenvalue problems for time dependent problems in the Floquet representation [3, 4, 5, 6]. Most of the known results are valid for sufficiently small perturbation of some simple (integrable) system. The phenomena arising for large perturbations, in particular critical perturbations at which a given torus loses its stability, have been discussed in the framework of some approximate schemes inspired in renormalization group ideas [7, 8, 9]. In this framework, an iterat…
Spacetime curvature and Higgs stability after inflation
2015
We investigate the dynamics of the Higgs field at the end of inflation in the minimal scenario consisting of an inflaton field coupled to the Standard Model only through the non-minimal gravitational coupling $\xi$ of the Higgs field. Such a coupling is required by renormalisation of the Standard Model in curved space, and in the current scenario also by vacuum stability during high-scale inflation. We find that for $\xi\gtrsim 1$, rapidly changing spacetime curvature at the end of inflation leads to significant production of Higgs particles, potentially triggering a transition to a negative-energy Planck scale vacuum state and causing an immediate collapse of the Universe.
To d , or not to d : recent developments and comparisons of regularization schemes
2017
We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them.
Weight Systems from Feynman Diagrams
1996
We find that the overall UV divergences of a renormalizable field theory with trivalent vertices fulfil a four-term relation. They thus come close to establish a weight system. This provides a first explanation of the recent successful association of renormalization theory with knot theory.
Entropy Production during Asymptotically Safe Inflation
2011
The Asymptotic Safety scenario predicts that the deep ultraviolet of Quantum Einstein Gravity is governed by a nontrivial renormalization group fixed point. Analyzing its implications for cosmology using renormalization group improved Einstein equations we find that it can give rise to a phase of inflationary expansion in the early Universe. Inflation is a pure quantum effect here and requires no inflaton field. It is driven by the cosmological constant and ends automatically when the renormalization group evolution has reduced the vacuum energy to the level of the matter energy density. The quantum gravity effects also provide a natural mechanism for the generation of entropy. It could eas…
From Big Bang to Asymptotic de Sitter: Complete Cosmologies in a Quantum Gravity Framework
2005
Using the Einstein-Hilbert approximation of asymptotically safe quantum gravity we present a consistent renormalization group based framework for the inclusion of quantum gravitational effects into the cosmological field equations. Relating the renormalization group scale to cosmological time via a dynamical cutoff identification this framework applies to all stages of the cosmological evolution. The very early universe is found to contain a period of ``oscillatory inflation'' with an infinite sequence of time intervals during which the expansion alternates between acceleration and deceleration. For asymptotically late times we identify a mechanism which prevents the universe from leaving t…
Pair creation in electric fields, anomalies, and renormalization of the electric current
2018
We investigate the Schwinger pair production phenomena in spatially homogeneous strong electric fields. We first consider scalar QED in four-dimensions and discuss the potential ambiguity in the adiabatic order assignment for the electromagnetic potential required to fix the renormalization subtractions. We argue that this ambiguity can be solved by invoking the conformal anomaly when both electric and gravitational backgrounds are present. We also extend the adiabatic regularization method for spinor QED in two-dimensions and find consistency with the chiral anomaly. We focus on the issue of the renormalization of the electric current $\langle j^\mu \rangle$ generated by the created pairs.…
The 1-loop effective potential for the Standard Model in curved spacetime
2018
The renormalisation group improved Standard Model effective potential in an arbitrary curved spacetime is computed to one loop order in perturbation theory. The loop corrections are computed in the ultraviolet limit, which makes them independent of the choice of the vacuum state and allows the derivation of the complete set of $\beta$-functions. The potential depends on the spacetime curvature through the direct non-minimal Higgs-curvature coupling, curvature contributions to the loop diagrams, and through the curvature dependence of the renormalisation scale. Together, these lead to significant curvature dependence, which needs to be taken into account in cosmological applications, which i…
Do we Observe Quantum Gravity Effects at Galactic Scales?
2005
The nonperturbative renormalization group flow of Quantum Einstein Gravity (QEG) is reviewed. It is argued that there could be strong renormalization effects at large distances, in particular a scale dependent Newton constant, which mimic the presence of dark matter at galactic and cosmological scales.