Rescriptive and Descriptive Gauge Symmetry in Finite-Dimensional Dynamical Systems

Details Rescriptive and Descriptive Gauge Symmetry in Finite-Dimensional Dynamical Systems Rescriptive and Descriptive Gauge Symmetry in Finite-Dimensional Dynamical Systems

Feb 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007aipc..886...42g&link_type=abstract

NEW TRENDS IN ASTRODYNAMICS AND APPLICATIONS III. AIP Conference Proceedings, Volume 886, pp. 42-67 (2007).

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Symmetry And Conservation Laws, Gauge Field Theories, Particle-Theory And Field-Theory Models Of The Early Universe

Scientific paper

Gauge theories in physics constitute a fundamental tool for modeling interactions among electromagnetic, weak and strong forces. They have been used in a myriad of fields, ranging from sub-atomic physics to cosmology. The basic mathematical tool generating the gauge theories is that of symmetry, i.e. a redundancy in the description of the system. Although symmetries have long been recognized as a fundamental tool for solving ordinary differential equations, they have not been formally categorized as gauge theories. In this paper, we show how simple systems described by ordinary differential equations are prone to exhibit gauge symmetry, and discuss a few practical applications of this approach. In particular, we utilize the notion of gauge symmetry to question some common engineering misconceptions of chaotic and stochastic phenomena, and show that seemingly ``disordered'' (deterministic) or ``random'' (stochastic) behaviors can be ``ordered''. This brings into play the notion of observation; we show that temporal observations may be misleading when used for chaos detection. From a practical standpoint, we use gauge symmetry to considerably mitigate the numerical truncation error of numerical integrations.

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