Group theory aspects of chaotic strings

3Quantum: Algebra Geometry Information

物理学;数学

Groote, S.^1,2 ; Saar, R.^2

Institut für Physik, Johannes-Gutenberg-Universität, Staudinger Weg 7, Mainz

55099, Germany^1

Füüsika Instituut, Tartu Ülikool, Ravila 4c, Tartu

50411, Estonia^2

关键词: Chebyshev map;    Coupled map lattices;    Cyclic group;    Dynamical phenomena;    Galois theory;    Group structure;    Rich structure;    Space time;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/532/1/012006/pdf
DOI  :  10.1088/1742-6596/532/1/012006

来源: IOP

【 摘 要 】

Chaotic strings are a special type of non-hyperbolic coupled map lattices, exhibiting a rich structure of complex dynamical phenomena with a surprising correspondence to physical contents. Chaotic strings are generated by the Chebyshev maps T2(φ) and T3(φ). In this paper we connect the Chebyshev maps via the Galois theory to the cyclic groups Z2and Z3and give some ideas how this fundamental connection might lead to the emergence of the familiar Lie group structure of particle physics and, finally, even to the emergence of space-time. The Z3-graded cubic and ternary algebras presented here have been introduced by R. Kerner in 1991 and then developed and elaborated in collaboration with many researches. We present here the most important results associated with these papers.