Chaos in Constrained System


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. 

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Nelson, M (2021). Chaos in Constrained System. Afribary. Retrieved from

MLA 8th

Nelson, Mike "Chaos in Constrained System" Afribary. Afribary, 14 Apr. 2021, Accessed 21 Jul. 2024.


Nelson, Mike . "Chaos in Constrained System". Afribary, Afribary, 14 Apr. 2021. Web. 21 Jul. 2024. < >.


Nelson, Mike . "Chaos in Constrained System" Afribary (2021). Accessed July 21, 2024.