Related papers: $\Phi^4$ theory is trivial

We use a very simple version of the optimized (linear) $\delta $ - expansion by scaling the free part of the Lagrangian with a variational parameter. This method is well suited to calculate the renormalized coupling constant in terms of the…

We compute the renormalized trajectory of $\phi^4_4$-theory by perturbation theory in a running coupling. We use an exact infinitesimal renormalization group. The expansion is put into a form which is manifestly independent of the scale…

We investigate the statement ``all automorphisms of $\mathcal P(\lambda)/[\lambda]^{<\lambda}$ are trivial''. We show that MA implies the statement for regular uncountable $\lambda<2^{\aleph_0}$; that the statement is false for measurable…

We have done a study of the zero-dimensional $\lambda\phi^{4}$ model. Firstly, we exhibit the partition function as a simple exact expression in terms of the Macdonald's function for $Re(\lambda)>0$. Secondly, an analytic continuation of…

The simplest non commutative renormalizable field theory, the $\phi_4^4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe at one loop, as shown by H. Grosse and R. Wulkenhaar. We extend this result up to…

Simple algebraic groups of type $F_4$ defined over a field $k$ are the full automorphism groups of Albert algebras over $k$. Let $A$ be an Albert algebra over a field $k$ of arbitrary characteristic. We prove that there is an isotope…

Perturbation theory of a large class of scalar field theories in $d<4$ can be shown to be Borel resummable using arguments based on Lefschetz thimbles. As an example we study in detail the $\lambda \phi^4$ theory in two dimensions in the…

The renormalized trajectory of massless $\phi^4$-theory on four dimensional Euclidean space-time is investigated as a renormalization group invariant curve in the center manifold of the trivial fixed point, tangent to the…

The simplest non commutative renormalizable field theory, the $\phi_4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe up to three loops, as shown by H. Grosse and R. Wulkenhaar, M. Disertori and V.…

We have constructed the mean-field trivial solution of the $\varphi^4$ theory $O(N)$ model in four dimensions in two previous papers using the flow equations of the renormalization group. Here we establish a relation between the trivial…

According to recent results, the Gell-Mann - Low function \beta(g) of four-dimensional \phi^4 theory is non-alternating and has a linear asymptotics at infinity. According to the Bogoliubov and Shirkov classification, it means possibility…

We argue that massless (lambda Phi^4)_4 is "trivial" without being entirely trivial. It has a non-trivial effective potential which leads to spontaneous symmetry breaking, but the particle excitations above the broken vacuum are…

We review our recent construction of the $\phi^4$-model on four-dimensional Moyal space. A milestone is the exact solution of the quartic matrix model $Z[E,J]=\int d\Phi \exp(tr(J\Phi- E\Phi^2 -(\lambda/4) \Phi^4))$ in terms of the solution…

I give a review and progress report on studies of lattice QED. I emphasize analytical results and methods that are applied in data analysis. Also, I derive some bounds for the critical exponents and establish their connection with scaling…

We present the main ideas and techniques of the proof that the duality-covariant four-dimensional noncommutative \phi^4-model is renormalisable to all orders. This includes the reformulation as a dynamical matrix model, the solution of the…

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…

Assuming triviality of the 4-dimensional $\lambda \phi ^4$-theory we compute the effective potential by means of a self consistent Feynman-Bogoliubov method. This potential $U_{eff}^{FB}$ depends on a UV-cutoff, which is fixed by a…

We show that principal bundles for a semisimple group on an arbitrary affine curve over an algebraically closed field are trivial, provided the order of $\pi_1$ of the group is invertible in the ground field, or if the curve has semi-normal…

Triviality of $\phi^4$ theory in four dimensions can be avoided if the bare coupling constant is negative in the UV. Theories with negative coupling can be put on the lattice if the integration domain for $\phi(x)$ is contour-deformed from…

It is conjectured by de Jong that, if $X$ is a connected projective smooth variety over an algebraically closed field $k$ of characteristic $p>0$ with trivial etale fundamental group, any convergent isocrystal $\mathcal{E}$ on $X$ is…