 Baker (2016) and Swanson (2017) note that LQFT makes false or unproven assumptions such as the convergence of certain infinite sums in perturbation theory. Dyson (1952) gives a heuristic argument that quantum electrodynamic perturbation series do not converge. Baker and Swanson also argue that the use of long distance cutoffs is at odds with cosmological theory and astronomical observations which suggest that the universe is spatially infinite. Even in the weak coupling limit where perturbation theory can be formally applied, it is not clear when the perturbative QFT gives an accurate approximation of the underlying physics. In the interacting \(\phi^4\) theory, when the dimension is less than 4 for Minkowski spacetime, the theory is nontrivial, but when the dimension is greater than 4, the renormalized perturbation series is asymptotic to a free field theory even though it appears to describe nontrivial interactions. When there are 4 dimensions, the theory is also trivial if additional technical assumptions hold (see Swanson 2017 (p. 3) for more details).