Beyond the initial value problem in multi-temporal wave-like equations, the existence of causality problems (we could give up if extra time directions are not too large, I think), or the instability issues related to energy in these theories (generally, it is said that these theories have spectra not bounded from below causing instabilities), are there any (non-observational only) other theoretical issue to consider more seriously multi-time theories?
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More on multiple time directions: https://physics.stackexchange.com/q/43322/2451 , https://physics.stackexchange.com/q/43630/2451 – Qmechanic Jan 20 '18 at 16:28