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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?

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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/43322/2451 , physics.stackexchange.com/q/43630/2451 and links therein. $\endgroup$
    – Qmechanic
    Apr 6 at 12:06
  • $\begingroup$ @Qmechanic thanks, but my question is more about a List of theories that need a signature $(p,q)$ with $p,q\geq2$. One of your question deals with "intuition of more times" and the other with a signature $2,2$ or something related to general relativity. I would like to have a more general list, without specify "why" more time-direction are needed, nor "what is their meaning". I could not find a "full" list on those question $\endgroup$ Apr 6 at 12:37