Related papers: Constructive Renormalization of 2-dimensional Gros…
We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. The BRS formulation of gauge invariance in this framework,…
It is well known that the mathematical structure underlying renormalization in perturbative quantum field theory is based on a Hopf algebra of Feynman diagrams. A precondition for this is locality of the field theory. Consequently, one…
We perform the complete one-loop renormalization of a general two-Higgs-doublet model. We present all the vertices for this model including the ones in the scalar sector and calculate all the counterterms of the theory.
We extend the scalar-tensor reconstruction techniques for classical cosmology frameworks, in the context of loop quantum cosmology. After presenting in some detail how the equations are generalized in the loop quantum cosmology case, we…
In the first part of this lecture, the 1/N expansion technique is illustrated for the case of the large-N sigma model. In large-N gauge theories, the 1/N expansion is tantamount to sorting the Feynman diagrams according to their degree of…
Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these…
This article provides a Wilsonian description of the perturbatively renormalizable Tensorial Group Field Theory introduced in arXiv:1303.6772 [hep-th] (Commun. Math. Phys. 330, 581-637). It is a rank-3 model based on the gauge group SU(2),…
The first renormalisable quantum field theories on non-commutative space have been found recently. We review this rapidly growing subject.
We perform an all-order resurgence analysis of a quantum field theory renormalon that contributes to an anomalous dimension in six-dimensional scalar $\phi^3$ theory and is governed by a third-order nonlinear differential equation. We…
In the practice of physics model building, the process of renormalization, resummation, and anomaly cancellation is to incrementally repair initially ill-defined Lagrangian quantum field theories. Impressive as this is, one would rather…
In this paper the massive neutrinos model arising due to the Snyder noncommutative geometry, proposed recently by the author is partially developed. By straightforward calculation it is shown that the masses of the chiral left- and…
The main part of this presentation is a review of the previous original works on the perturbative covariant approach to the $2$-dimensional quantum gravity. We discuss the renormalization of the two-dimensional dilaton gravity in a harmonic…
We discuss the non-anticommutative (N=1/2) supersymmetric U(1) gauge theory in four dimensions, including a superpotential. We perform the one-loop renormalisation of the model, including the complete set of terms necessary for…
We examine several different types of five dimensional stationary spacetimes with bulk scalar fields and parallel 3-branes. We study different methods for avoiding the appearance of spacetime singularities in the bulk for models with and…
We propose a general formulation of perturbative quantum field theory on (finitely generated) projective modules over noncommutative algebras. This is the analogue of scalar field theories with non-trivial topology in the noncommutative…
We consider some typical gauge models in the causal approach: Yang-Mills and pure massless gravity up to the second order of the perturbation theory. We prove that the loop contributions are coboundaries, up to super-renormalizable terms in…
A modification of perturbation theory, known as delta-expansion (variationally improved perturbation), gave rigorously convergent series in some D=1 models (oscillator energy levels) with factorially divergent ordinary perturbative…
Solving the exact renormalisation group equation a la Wilson-Polchinski perturbatively, we derive a power-counting theorem for general matrix models with arbitrarily non-local propagators. The power-counting degree is determined by two…
We show a Wolfram model whose renormalization generates a sequence of approximations of a wave function having the Pauli-x matrix as Hamiltonian.
An improved $\eps$ expansion in the $d$-dimensional ($d > 2$) stochastic theory of turbulence is constructed at two-loop order which incorporates the effect of pole singularities at $d \to 2$ in coefficients of the $\eps$ expansion of…