Related papers: The renormalization group equations revisited
We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced…
Techniques based on $n$-particle irreducible effective actions can be used to study systems where perturbation theory does not apply. The main advantage, relative to other non-perturbative continuum methods, is that the hierarchy of…
We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced…
In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper,…
Effective potential for scalar $\lambda\phi^4$ theory is obtained using the exact renormalization group method which includes both the usual one-loop contribution as well as the dominant higher loop effects. Our numerical calculation…
We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space…
We consider all radiative corrections to the total electron-positron cross section showing how the renormalization group equation can be used to sum the logarithmic contributions in two ways. First of all, one can sum leading-log etc.…
A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration…
For theories with multiple couplings we construct simple expressions for the four-dimensional (or, in general, integer-dimensional) renormalization constants assuming that all divergences are logarithmical. These expressions allow relating…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
Explicit divergences and counterterms do not appear in the differential renormalization method, but they are concealed in the neglected surface terms in the formal partial integration procedure used. A systematic real space cutoff procedure…
The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…
We revisit the renormalisation of models with two U(1) gauge symmetries, in a formulation with non-canonical gauge kinetic terms which is covariant under field reparametrisations among the two gauge bosons. This approach is convenient to…
Two-loop renormalization group equations in gauge theories with multiple U(1) groups are presented. Instead of normalizing the abelian gauge fields in canonical forms, we retain kinetic-mixing terms and treat the mixing coefficients as free…
Renormalization group (RG) and resummation techniques have been used in $N$-component $\phi^4$ theories at fixed dimensions below four to determine the presence of non-trivial IR fixed points and to compute the associated critical…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
We derive the 1-loop Renormalization Group Equations for the parameters of the Minimal Supersymmetric Standard Model (MSSM) taking into account the successive decoupling of each sparticle below its threshold. This is realized by a step…
We discuss a renormalization scheme for relativistic baryon chiral perturbation theory which provides a simple and consistent power counting for renormalized diagrams. The method involves finite subtractions of dimensionally regularized…
We consider a symmetric scalar theory with quartic coupling in 4-dimensions and compare the standard 2PI calculation with a modified version which uses a functional renormalization group method. The set of integral differential equations…
The complete set of two-loop renormalization group equations in general gauge field theories is presented. This includes the \beta functions of parameters with and without a mass dimension.