Related papers: The renormalized $\phi^4_4$-trajectory by perturba…
We study the renormalization invariant trajectory of the $\phi^4$-perturbation of the free field fixed point in the hierarchical approximation. We parametrize it by a running $\phi^4$-coupling $g$ with linear step $\beta$-function. We…
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…
In this paper we provide a new proof that the Grosse-Wulkenhaar non-commutative scalar Phi^4_4 theory is renormalizable to all orders in perturbation theory, and extend it to more general models with covariant derivatives. Our proof relies…
We study a renormalized coupling g and mass m in four dimensional phi^4 theory on tori with finite size z=mL. Precise numerical values close to the continuum limit are reported for z=1,2,4, based on Monte Carlo simulations performed in the…
We study the standard one-component $\varphi^4$-theory in four dimensions. A renormalized coupling is defined in a finite size renormalization scheme which becomes the standard scheme of the broken phase for large volumes. Numerical…
The renormalization group is applied to the phi4 model in the symmetry broken phase in order to identify different scaling regimes. The new scaling laws reflect nonuniversal behavior at the phase transition. The extension of the analysis to…
We propose a novel diagrammatic method for computing transport coefficients in relativistic quantum field theory. The self-consistent equation for summing the diagrams with pinch singularities has a form of a linearized kinetic equation as…
We study perturbative aspects of noncommutative field theories. This work is arranged in two parts. First, we review noncommutative field theories in general and discuss both canonical and path integral quantization methods. In the second…
The general prescription for constructing the continuum limit of a field theory is explained using Wilson's renormalization group. We then formulate the renormalization group in perturbation theory and apply it to the four dimensional phi4…
For the anisotropic $[u (\sum_{i=1^N {\phi}_i^2)^2+v \sum_{i=1^N \phi_i^4]$-theory with {$N=2,3$} we calculate the imaginary parts of the renormalization-group functions in the form of a series expansion in $v$, i.e., around the isotropic…
We present a new approach to calculation of anomalous dimensions in the framework of $\epsilon$-expansion and renormalization group method. This approach allows one to skip the calculation of renormalization constants and express anomalous…
We develop a non-perturbative functional framework for computing real-time correlation functions in strongly correlated systems. The framework is based on the spectral representation of correlation functions and dimensional regularisation.…
A finite-size scaling theory for the $\phi^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the…
The graphical extrapolation procedure to infinite order of variational perturbation theory in a recent calculation of critical exponents of three-dimensional $\phi^4$-theories at infinite couplings is improved by another way of plotting the…
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…
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…
Using the renormalization group techniques it was previously shown that the perturbative effective potential in the $\mathcal{O}(N)$ symmetric $\phi^4$ theory, massless scalar electrodynamics as well as in the conformal limit of the…
A gradient flow equation for $\lambda\phi^{4}$ theory in $D=4$ is formulated. In this scheme the gradient flow equation is written in terms of the renormalized probe variable $\Phi(t,x)$ and renormalized parameters $m^{2}$ and $\lambda$ in…
We discuss the renormalizability of Phi-derivable approximations in scalar phi^4 theory in four dimensions. The formalism leads to self-consistent equations for the 2-point and the 4-point functions which are plagued by ultraviolet…
We present a new real space renormalization-group map, on the space of probabilities, to study the renormalization of the SUSY \phi^4. In our approach we use the random walk representation on a lattice labeled by an ultrametric space. Our…