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In recent years, $f(Q)$ gravity has enjoyed considerable attention in theliterature and important results have been obtained. However, the question ofhow many physical degrees of freedom the theory propagates -- and how thisnumber may depend on the form of the function $f$ -- has not been answeredsatisfactorily. In this article we show that a Hamiltonian analysis based onthe Dirac-Bergmann algorithm -- one of the standard methods to address thistype of question -- fails. We isolate the source of the failure, show thatother commonly considered teleparallel theories of gravity are affected by thesame problem, and we point out that the number of degrees of freedom obtainedin Phys. Rev. D 106 no. 4, (2022) by K. Hu, T. Katsuragawa, and T. Qui (namelyeight), based on the Dirac-Bergmann algorithm, is wrong. Using a differentapproach, we show that the upper bound on the degrees of freedom is seven.Finally, we propose a more promising strategy for settling this importantquestion.

Hamiltonian Analysis of $f(Q)$ Gravity and the Failure of the Dirac-Bergmann Algorithm for Teleparallel Theories of Gravity