Hidden Symmetries, Symmetry-Breaking and Emergence of Complexity

Abstract

Symmetry presumes the presence of a certain set of representations to be acted upon and transformed among themselves. The phase-space point in classical mechanics and the wavefunction in quantum mechanics are two of the most quoted representations or, more precisely, state-representations in physics. However, representation pointing to a physical object already assumes by itself an implicit operation of getting it while referring to the object in the first place. Any representation of a physical object is intrinsically dynamic in the act of associating the object to its representation. The present implicit dynamics underlying the representation now makes a sharp contrast to the dynamics in terms of representations alone, At issue is how the transformation dynamics of a physical object to its representation would influence the dynamics of representations themselves, especially with regard to its dynamic symmetry. This interference would become most acute when it is focused upon how to conceive of the physical origin of symmetry-breaking acting upon the dynamic symmetry that those representations are supposed to maintain.