Related papers: A Short Lecture on Divergences
We compare the results of renormalization-group and lattice studies for the properties of the electroweak phase transition. This comparison reveals the mechanisms that underlie the phenomenology of the phase transition.
A perturbative renormalization group method is used to obtain steady-state density profiles of a particle non-conserving asymmetric simple exclusion process. This method allows us to obtain a globally valid solution for the density profile…
Early developments leading to renormalizable non-Abelian gauge theories for the weak, electromagnetic and strong interactions, are discussed from a personal viewpoint. They drastically improved our view of the role of field theory, symmetry…
These lecture notes provide a unified overview of most known canonical desingularization methods in characteristic zero. It starts with discussing the classical method, and then proceeds with the recently discovered ones: logarithmic…
This is a kind of introduction to some basic topics in analysis, some of which would be covered in standard graduate courses, and some not. However, an important difference is that not much in the way of prerequisites are needed, beyond…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
We derive the renormalization group equations for a generic nonrenormalizable theory. We show that the equations allow one to derive the structure of the leading divergences at any loop order in terms of one-loop diagrams only. In chiral…
Introductory lectures on the phenomenology of the minimal supersymmetric Standard Model. The emphasis is on general signatures for supersymmetry and on the motivation for constructing supersymmetric models. These lectures are intended for…
The renormalization group has played an important role in the physics of the second half of the twentieth century both as a conceptual and a calculational tool. In particular it provided the key ideas for the construction of a qualitative…
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
This very short correction notes a gap in an argument of an earlier paper, and also provides a theorem of similar flavor to the main result of that paper.
The divergent part of the generating functional of the Resonance Chiral Theory is evaluated up to one loop when one multiplet of scalar an pseudoscalar resonances are included and interaction terms which couple up to two resonances are…
In this paper, we study the structure of a generalized near-group fusion category and classified it when it is slightly degenerate.
This is a copy of the 2009 Princeton University thesis which examined various aspects of gauge/gravity duality, including renormalization group flows, phase transitions of the holographic entanglement entropy, and instabilities associated…
This article presents a tutorial introduction to a recently developed real-time renormalization group method. It describes nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We illustrate the technique…
Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here we show that renormalization group flow equations can be used to construct the information metric and…
In previous studies, we proposed a scaling ansatz for electron-electron interactions under renormalization group transformation. With the inclusion of phonon-mediated interactions, we show that the scaling ansatz, characterized by the…
In the Yukawa model with two different mass scales the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. Considering fermion-fermion scattering as an example, a basic one-loop…
In the past two decades or so, we have learned how to understand crackling noise in a wide variety of systems. We review here the basic ideas and methods we use to understand crackling noise - critical phenomena, universality, the…
Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the…