Abstract
Chaos poses technical challenges to constrained Hamiltonian systems. This is an important topic for discussion, because general relativity in its Hamiltonian formulation is a constrained system, and there is strong evidence that it exhibits chaotic features. We review concepts in gauge systems and their association with Hamiltonian constraints, relational Dirac observables as gauge-invariant encodings of physical information, and chaos in unconstrained Hamiltonian systems. We then construct a non-integrable, ergodic toy model, and with it explicitly illustrate the non-existence of a maximal set of Dirac observables and a solution space that fails to be a manifold. The potential consequences of these qualitative features of a chaotic constrained Hamiltonian system for general relativity and the quest for its quantum theory are deliberated.
Nelson, M (2021). Chaos in Constrained System. Afribary. Retrieved from https://afribary.com/works/chaos-in-constrained-system
Nelson, Mike "Chaos in Constrained System" Afribary. Afribary, 14 Apr. 2021, https://afribary.com/works/chaos-in-constrained-system. Accessed 19 May. 2024.
Nelson, Mike . "Chaos in Constrained System". Afribary, Afribary, 14 Apr. 2021. Web. 19 May. 2024. < https://afribary.com/works/chaos-in-constrained-system >.
Nelson, Mike . "Chaos in Constrained System" Afribary (2021). Accessed May 19, 2024. https://afribary.com/works/chaos-in-constrained-system