Related papers: The Effective Potential, the Renormalisation Group…
We study asymptotically non-free gauge theories and search for renormalization group invariant (i.e. technically natural) relations among the couplings which lead to successful gauge-Yukawa unification. To be definite, we consider a…
We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of…
Effective field theory of massive Yang-Mills fields interacting with fermions is considered. Perturbative renormalizability in the sense of effective field theory is shown. It is argued that the limit of vanishing vector boson mass leads to…
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…
Motivated by recent discussions of the string-theory landscape, we propose field-theoretic realizations of models with large numbers of vacua. These models contain multiple U(1) gauge groups, and can be interpreted as deconstructed versions…
Within an effective field theory framework we study heavy-quark--antiquark systems with a typical distance between the heavy quark and the antiquark smaller than $1/\Lambda_{\rm QCD}$. A suitable definition of the potential is given within…
In this work, we study the vacuum stability of the classical unstable $\left( -\phi^{4}\right) $ scalar field potential. Regarding this, we obtained the effective potential, up to second order in the coupling, for the theory in $1+1$ and…
The calculation of the effective potential for fixed-end and toroidal rigid $p$-branes is performed in the one-loop as well as in the $1/d$ approximations. The analysis of the involved zeta-functions (of inhomogeneous Epstein type) which…
One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton…
In the standard model the running quartic coupling becomes negative during its renormalization group flow, which destabilizes the vacuum. We consider U(1) extensions of the standard model, with an extra complex scalar field and a…
The equations for effective action for nonlinear $\sigma$ model are derived using DeWitt method in two forms - for generator of vertex parts $\Gamma$ and for generator of weakly connected parts $W$. Loop-expansion solutions to these…
We study the renormalization group flow in weak power counting (WPC) renormalizable theories. The latter are theories which, after being formulated in terms of certain variables, display only a finite number of independent divergent…
The optimized effective potential method is formulated as a convex minimization problem. This formulation does not require assumptions about $v$-representability nor functional differentiability. The formulation provides a natural framework…
Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's…
In this paper we start a systematic study of quantum field theory on random trees. Using precise probability estimates on their Galton-Watson branches and a multiscale analysis, we establish the general power counting of averaged Feynman…
Following the previously developed approach to the calculation of quantum corrections to the effective potential in arbitrary scalar field theories in the leading logarithmic approximation, we extended it to the next-to-leading order. Based…
Massless $\phi^{4}$-theory is investigated in zero and four space-time dimensions. Path-integral linearisation of the $\phi ^{4}$-interaction defines an effective theory, which is investigated in a loop-expansion around the mean field. In…
We revisit the formalism for tunneling in quantum field theory developed by Coleman and collaborators. In particular using the generalization of WKB methods for tunneling in quantum mechanics we avoid the problems with negative eigenvalues…
Vacuum energies are computed in light-cone field theories to obtain effective potentials which determine vacuum condensate. Quantization surfaces interpolating between the light-like surface and the usual spatial one are useful to define…
We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows to describe the effective potential as a function of both scalar field…