Related papers: Can negative bare couplings make sense? The $\vec{…
Perturbative renormalization provides the bedrock of understanding quantum field theories. In this work, I point out an alternative way of renormalizing quantum field theories, which is naturally encountered and well known for the case of…
We try to use scale-invariance and the large-N limit to find a non-trivial 4d O(N) scalar field model with controlled UV behavior and naturally light scalar excitations. The principle is to fix interactions by requiring the effective action…
An alternative model to the trivial $\phi^4$-theory of the standard model of weak interactions is suggested, which embodies the Higgs-mechanism, but is free of the conceptual problems of standard $\phi ^4$-theory. We propose a N-component,…
We continue the study, initiated in arXiv:1404.1094, of the $O(N)$ symmetric theory of $N+1$ massless scalar fields in $6-\epsilon$ dimensions. This theory has cubic interaction terms $\frac{1}{2}g_1 \sigma (\phi^i)^2 + \frac{1}{6}g_2…
We observe that probing certain classical field theories by external sources uncovers the underlying renormalization group structure, including the phenomenon of dimensional transmutation, at purely-classical level. We perform this study on…
With the help of variational perturbation theory we continue the renormalization constants $\phi^4$-theories in $4- \epsilon$ dimensions to strong bare couplings $g_0$ and find their power behavior in $g_0$, thereby determining all critical…
Using the effective potential, we study the one-loop renormalization of a massive self-interacting scalar field at finite temperature in flat manifolds with one or more compactified spatial dimensions. We prove that, owing to the…
We show that a recent analysis in the strong coupling limit of the $\lambda\phi^4$ theory proves that this theory is indeed trivial giving in this limit the expansion of a free quantum field theory. We can get in this way the propagator…
In the literature, the asymptotic freedom property of the $(-\phi^{4})$ theory is always concluded from real-line calculations while the theory is known to be a non-real-line one. In this article, we test the existence of the asymptotic…
In 1973, Coleman and Gross proved that in four dimensions, only non-abelian gauge theories can have asymptotic freedom. More recently, Aizenman and Duminil-Copin proved that four dimensional scalar field theories are quantum trivial in the…
We make a detailed analysis of the spontaneous $Z_{2}$-symmetry breaking in the two dimensional real $\phi^{4}$ theory with the tensor renormalization group approach, which allows us to take the thermodynamic limit easily and determine the…
We consider ${\rm U}(1)$-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously…
By the concurrent use of two different resummation methods, the composite operator formalism and the Dyson-Schwinger equation, we re-examinate the behavior at finite temperature of the O(N)-symmetric $\lambda\phi^{4}$ model in a generic…
We study the thermal phase transitions of a generic real scalar field, without a $Z_2$-symmetry, referred to variously as an inert, sterile or singlet scalar, or $\phi^3+\phi^4$ theory. Such a scalar field arises in a wide range of models,…
We revisit scalar $\phi^4$ theory and construct a reorganized perturbative expansion in which the kinetic operator, rather than the quartic interaction, is treated as the perturbation. Starting from the exactly solvable $0$-dimensional…
Theory of massless scalar field $\phi$ with interaction $g \phi^3$ in six-dimensional space is considered. A possibility of initial scale invariance breaking, which results in a spontaneous arising of effective interaction $G \phi^4$, is…
We study the phase structure of a 4D complex scalar field theory with a potential V(Phi) = | Lambda^3 / Phi - Lambda Phi |^2 at zero and at finite temperature. The model is analyzed by mean field and Monte Carlo methods. At zero temperature…
We study the critical behaviour of symmetric $\phi^4_4$ theory including irrelevant terms of the form $\phi^{4+2n}/\Lambda_0^{2n}$ in the bare action, where $\Lambda_0$ is the UV cutoff (corresponding e.g. to the inverse lattice spacing for…
We discuss a D-dimensional Euclidean scalar field interacting with a scale invariant quantized metric. We assume that the metric depends on d-dimensional coordinates where d<D. We show that the interacting quantum fields have more regular…
We study interacting fixed points and phase diagrams of simple and semi-simple quantum field theories in four dimensions involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. Particular emphasis is put on new…