  By comparing with recently available experimental data from several groups,
we critically discuss the manifestation of continuum many body interaction
effects in twisted bilayer graphene (tBLG) with small twist angles and low
carrier densities, which arise naturally within the Dirac cone approximation
for the non-interacting band structure. We provide two specific examples of
such continuum many body theories: one involving electron-phonon interaction
and one involving electron-electron interaction. In both cases, the
experimental findings are only partially quantitatively consistent with rather
clear-cut leading-order theoretical predictions based on well-established
continuum many body theories. We provide a critical discussion, based mainly on
the currently available tBLG experimental data, on possible future directions
for understanding many body renormalization involving electron-phonon and
electron-electron interactions in the system. One definitive conclusion based
on the comparison between theory and experiment is that the leading order
1-loop perturbative renormalization group theory completely fails to account
for the electron-electron interaction effects in the strong-coupling limit of
flatband moir\'e tBLG system near the magic twist angle even at low doping
where the Dirac cone approximation should apply. By contrast, approximate
nonperturbative theoretical results based on Borel-Pad\'e resummation or $1/N$
expansion seems to work well compared with experiments, indicating rather small
interaction corrections to Fermi velocity or carrier effective mass. For
electron-phonon interactions, however, the leading-order continuum theory works
well except when van Hove singularities in the density of states come into
play.

Mesoscale and Nanoscale Physics;Strongly Correlated Electrons