Group theory aspects of chaotic strings

Renormalization aspects of chaotic strings

Chaotic strings are a class of non-hyperbolic coupled map lattices, exhibiting a rich structure of complex dynamical phenomena with a surprising correspondence to physical contents. In this paper we introduce different types and models for chaotic strings, where 2B-strings with finite length are considered in detail. We demonstrate possibilities to extract renormalized quantities, which are exp...

Renormalization group approach to chaotic strings

Coupled map lattices of weakly coupled Chebychev maps, so-called chaotic strings, have a profound physical meaning in terms of dynamical models of vacuum fluctuations in stochastically quantized field theories. Here we present analytic results for the invariant density of chaotic strings, as well as for the coupling parameter dependence of given observables of the chaotic string such as the vac...

Dynamics of chaotic strings

Some aspects of group theory

Our goal in this section will be to collect some standard examples of finite groups. The main emphasis will be on realizing them as subgroups of GL(n,R) or GL(n,C). Cyclic groups: For a natural number n, let Z/nZ be the standard cyclic group of order n. We denote its elements by 0, 1, . . . , n − 1, and 1 is a generator. Another model for the cyclic group of order n is the nth roots of unity, o...

Discrete Symmetries of Chaotic Strings

Chaotic strings are particular classes of coupled map lattices that can serve as models for vacuum fluctuations in stochastically quantized field theories. They have been previously shown to distinguish standard model coupling parameters as corresponding to states of strongest possible chaotic behaviour and vanishing nearest-neighbour correlation. In this paper we look at discrete symmetry tran...