Related papers: Renormalization and Knot Theory
We contruct here the Hopf algebra structure underlying the process of renormalization of non-commutative quantum field theory.
We apply the renormalization group theory to the dynamical systems with the simplest example of basic biological motifs. This includes the interpretation of complex networks as the perturbation to simple network. This is the first step to…
We study the gravitational dressing of renormalizable two-dimensional field theories. Our main result is that the one-loop $\beta$-function is finitely renormalized by the factor ${k+2\over k+1}$, where $k$ is the central charge of the…
We investigate the relation between Connes-Kreimer Hopf algebra approach to renomalization and deformation quantization. Both approaches rely on factorization, the correspondence being established at the level of Wiener-Hopf algebras, and…
Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…
We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group…
We discuss the perturbative expansion of several one-loop improved renormalisation group equations. It is shown that in general the integrated renormalisation group flows fail to reproduce perturbation theory beyond one loop.
We consider the group formed by finite renormalizations as an infinite-dimensional Lie group. It is demonstrated that for the finite renormalization of the gauge coupling constant its generators $\hat L_n$ with $n\ge 1$ satisfy the…
We construct a superpotential for the general N=1/2 supersymmetric gauge theory coupled to chiral matter in the fundamental and adjoint representations, and investigate the one-loop renormalisability of the theories.
In this paper we are going to find a rooted tree representation from universal Hopf algebra of renormalization (in Connes-Marcolli's approach in the study of renormalizable Quantum Field Theories under the scheme minimal subtraction in…
We reformulate the quantization of the gravitational field and its sources, including the electric and magnetic fields as they appear in the knot algebra.
Manifestly invariant renormalization scheme for supersymmetric gauge theories is proposed. This scheme is applied to supersymmetric quantum electrodynamics.
We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of transverse index theory for foliations.
In this paper, a way of generalizing the tensor renormalization group(TRG) is proposed. Mathematically, the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is…
The renormalization method which is a type of perturbation method is extended to a tool to study weakly nonlinear time-delay systems. For systems with order-one delay, we show that the renormalization method leads to reduced systems without…
We look at sections of a function bundle over the space of linear differential operators. We find that one can construct an isomorphism between a certain quotient bundle and the fourier counterpart of the original bundle defined by formal…
By construction, gauge theories require gauge fixing. In conventional approaches to spontaneously broken gauge theories, the choice of the Unitary ('t Hooft) gauge involves the sacrifice of manifest renormalizability (unitarity). It is…
A simple backreaction problem in quantum mechanics, the full quantum anharmonic oscillator, and quantum parametric resonance are studied using Renormalization Group techniques for global asymptotic analysis. In this short note this…
The proof of one-loop renormalizability of the general Lorentz- and CPT-violating extension of quantum electrodynamics is described. Application of the renormalization-group method is discussed and implications for theory and experiment are…