Search results for "renormalization"
showing 10 items of 470 documents
A Positive Definite Advection Scheme Obtained by Nonlinear Renormalization of the Advective Fluxes
1989
Abstract A new method is developed to obtain a conservative and positive definite advection scheme that produces only small numerical diffusion. Advective fluxes are computed utilizing the integrated flux form of Tremback et al. These fluxes are normalized and then limited by upper and lower values. The resulting advection equation is numerically solved by means of the usual upstream procedure. The proposed treatment is not restricted to the integrated flux form but may also be applied to other known advection algorithms which are formulated in terms of advective fluxes. Different numerical tests are presented illustrating that the proposed scheme strongly reduces numerical and diffusion an…
NNLO QED contribution to the µe → µe elastic scattering
2020
We present the current status of the Next-to-Next-to-Leading Order QED contribution to theµescattering. Particular focus is given to the techniques involved to tackle the virtual amplitude and their automatic implementation. Renormalization of the amplitude will be also discuss in details.
Two-loop electroweak corrections to the ρ parameter beyond the leading approximation
1996
We show that in the framework of the pinch technique the universal part of the $\rho$ parameter can be meaningfully defined, beyond one loop. The universal part so obtained satisfies the crucial requirements of gauge-independence, finiteness, and process-independence, even when subleading contributions of the top quark are included. The mechanism which enforces the aforementioned properties is explained in detail, and several subtle field theoretical issues are discussed. Explicit calculations of the sub-leading two-loop corrections of order $O(G_{\mu}^{2}m^{2}_{t}M_{Z}^{2})$ are carried out in the context of an $SU(2)$ model, with $M_{W}=M_{Z}$, and various intermediate and final results a…
Inflation, quantum fields, and CMB anisotropies
2009
Revert field Inflationary cosmology has proved to be the most successful at predicting the properties of the anisotropies observed in the cosmic microwave background (CMB). In this essay we show that quantum field renormalization significantly influences the generation of primordial perturbations and hence the expected measurable imprint of cosmological inflation on the CMB. However, the new predictions remain in agreement with observation, and in fact favor the simplest forms of inflation. In the near future, observations of the influence of gravitational waves from the early universe on the CMB will test our new predictions.
Anharmonicity-induced polaron relaxation in GaAs/InAs quantum dots
2002
The anharmonicity-induced relaxation of a polaron in a quantum dot is analyzed using the Davydov diagonalization method, including the coherent renormalization of the relevant third-order phonon interaction. The resulting relaxation time for a small GaAs/InAs self-assembled quantum dot turns out to be a few times longer than that found previously by a perturbative method.
HIERARCHICAL MELTING OF ONE-DIMENSIONAL INCOMMENSURATE STRUCTURES
2016
We study the low—temperature properties of quasi one—dimensional, incommensurate structures which are described by a Frenkel—Kontorova—like model. A new type of renormalization method will be presented, which is determined by the continued fraction expansion of the incommensurability ratio ζ. (This method yields a hierarchy of renormalized Hamiltonians ϰ(n,p) describing the thermal behavior for temperatures T = O(T(n,p)), where T(n,p) follows from the continued fraction expansion of ζ. By means of this method the low—temperature specific heat c(T) and the static structure factor S(q) are calculated for fixed ζ. c(T) possesses a hierarchy of Schottky anomalies related to the rational approxi…
Geometry of the theory space in the exact renormalization group formalism
2018
We consider the theory space as a manifold whose coordinates are given by the couplings appearing in the Wilson action. We discuss how to introduce connections on this theory space. A particularly intriguing connection can be defined directly from the solution of the exact renormalization group (ERG) equation. We advocate a geometric viewpoint that lets us define straightforwardly physically relevant quantities invariant under the changes of a renormalization scheme.
Renormalization-group analysis for the transition to chaos in Hamiltonian systems
2002
Abstract We study the stability of Hamiltonian systems in classical mechanics with two degrees of freedom by renormalization-group methods. One of the key mechanisms of the transition to chaos is the break-up of invariant tori, which plays an essential role in the large scale and long-term behavior. The aim is to determine the threshold of break-up of invariant tori and its mechanism. The idea is to construct a renormalization transformation as a canonical change of coordinates, which deals with the dominant resonances leading to qualitative changes in the dynamics. Numerical results show that this transformation is an efficient tool for the determination of the threshold of the break-up of…
Is massless quantum electrodynamics a free-field theory?
1976
It is shown that if the photon wave-function renormalization constant is finite, then in the limit of zero fermion mass, quantum electrodynamics is a free- field theory.
Considerations concerning the renormalization of the electroweak sector of the standard model
1990
Abstract Examination of the structure of one-loop corrected amplitudes for arbitrary processes mediated by W, Z and γ in the simple renormalization framework previously discussed by the author, leads to natural choices for the renormalized self-energies and vertex corrections. They satisfy simple renormalization conditions and, as q2 → 0, the W and Z propagators approach the free expressions with a correction of O(αq2/mW2). The renormalization conditions allow us to circumvent certain ambiguities that arise, to O(α2), in current analyses of Δr and κ(q2). A useful simplified form for the Z propagator is presented.