Related papers: Renormalization and Knot Theory
I give an outline of recent applications of the renormalisation group to effective theories of nuclear forces, focussing on the use of a Wilsonian approach to analyse systems of two or three nonrelativistic particles.
Symbolic algebra relevant to the renormalization of gauge theories can be efficiently performed by machine using modern packages. We devise a scheme for representing and manipulating the objects involved in perturbative calculations of…
Renormalizability of the (minimal) single-fermion QED extension is investigated at all orders of perturbation theory in the framework of algebraic renormalization, a regularization-independent method. Relative to the standard QED, new…
The renormalization group method is applied for obtaining the asymptotic form of the wave function of the quantum anharmonic oscillator by resumming the perturbation series. It is shown that the resumed series is the cumulant of the naive…
In the framework of causal perturbation theory renormalization consists of the extension of distributions. We give the explicit form of a Lorentz invariant extension of a scalar distribution, depending on one difference of space time…
Connes and Kreimer have discovered a Hopf algebra structure behind renormalization of Feynman integrals. We generalize the Hopf algebra to the case of ribbon graphs, i.e. to the case of theories with matrix fields. The Hopf algebra is…
Koopman operator theory is shown to be directly related to the renormalization group. This observation allows us, with no assumption of translational invariance, to compute the critical exponents $\eta$ and $\delta$, as well as ratios of…
We review the techniques used to renormalize quantum field theories at several loop orders. This includes the techniques to systematically extract the infinities in a Feynman integral and the implementation of the algorithm within computer…
We first explain our joint work with Dirk Kreimer on the Hopf and Lie algebras of Feynman graphs. The conceptual meaning of the concrete computations of perturbative renormalisation is obtained from the Birkhoff decomposition in the…
We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending 't~Hooft's one-loop result. The method can also be used for theories with…
The requirement that duality and renormalization group transformations commute as motions in the space of a theory has recently been explored to extract information about the renormalization flows in different statistical and field…
Symmetry restoration is usually understood as a renormalization group induced phenomenon. In this context, the issue of whether one-loop RG equations can be trusted in predicting symmetry restoration has recently been the subject of much…
We demonstrate that the soft supersymmetry-breaking terms in a N=1 theory can be linked by simple renormalisation group invariant relations which are valid to all orders of perturbation theory. In the special case of finite N=1 theories,…
The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…
I outline why the renormalisation group is needed to analyse the scale dependence and hence determine the power counting for effective theories of strongly interacting systems. I summarise the results of several such analyses for two- and…
We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, renormalization scheme dependence of the scattering amplitude can only…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
In this note, I describe a formalism for treating knots as geometric spaces, and make an application to a simple statistical mechanics computation. The motivation for this study is the natural visual symmetry of the knot, and I describe how…
We describe in detail the constrained procedure of differential renormalization and develop the techniques required for one-loop calculations. As an illustration we renormalize Scalar QED and show that the two-, three- and four-point Ward…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…