Related papers: Some Observations on Broken Symmetries

This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…

Using resummation in perturbation theories at finite temperature or in non-equilibrium is unavoidable to obtain consistent results. Resummation, however, is often in conflict with renormalization. In this talk we give two possible solutions…

This is a further explanation of a new and simple renormalization approach recently proposed by the author (hep-th/9708104, Ref. [1], that is somewhat sketchy) for any ordinary QFT (whether renormalizable or not) in any spacetime dimension.…

The purpose of the present note is to review and improve the convergence of the renormalized winding fields.

We discuss all possible compactifications on flat three-dimensional smooth spaces. In particular, various fields are studied on a box with opposite sides identified, after two of them are rotated by $\pi$, and their spectra are obtained.…

We prove a general theorem on the stochastic convergence of appropriately renormalized models arising from nonlinear stochastic PDEs. The theory of regularity structures gives a fairly automated framework for studying these problems but…

I review various aspects of Feynman integrals, regularization and renormalization. Following Bloch, I focus on a linear algebraic approach to the Feynman rules, and I try to bring together several renormalization methods found in the…

We consider deformations of a conformal field theory that explicitly break some global symmetries of the theory. If the deformed theory is still a conformal field theory, one can exploit the constraints put by conformal symmetry to compute…

We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…

A novel algorithm is provided to couple a Galilean invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and…

Field theories in the presence of branes encounter localized divergences that renormalize brane couplings. The sources of these brane-localized divergences are understood as arising either from broken translation invariance, or from short…

The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results…

Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…

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…

Ladders of field polynomial differential forms obeying systems of descent equations and corresponding to observables and anomalies of gauge theories are renormalized. They obey renormalized descent equations. Moreover they are shown to have…

The standard approach to renormalization relies, technically, on the asymptotic perturbation of Gaussian measures embodied in Feynman diagram theory. From a mathematical standpoint this is not good enough, because thereby solving the…

We study and explore the symmetry properties of fermions coupled to dynamical torsion and electromagnetic fields. The stability of the theory upon radiative corrections as well as the presence of anomalies are investigated.

Reparametrization invariance being treated as a gauge symmetry shows some specific peculiarities. We study these peculiarities both from a general point of view and on concrete examples. We consider the canonical treatment of…

We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. Many of the presented…

We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory as well as number theory and…