I would like to understand better the role of indefinite metrics in physics. As far as I know, Lorentzian metric is the natural setting for Einstein's Relativity Theory. Somewhere I read something about theory modelling reality using more than one time directions, i.e. metric tensor of signature $(p,q)$ where $p,q\geq2$.
The question is the following: which theories actually need indefinite metric of non-Lorentzian signature?
