# Worldline Diffeomorphism invariance as the origin of the signature of the spacetime metric

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For a particle moving in a Spacetime with $n_{-}$ timelike dimensions and $n_{+}$ Spacelike dimensions , One can formulate actions that are invariant under the worldline diffeomorphism symmetry. The system is a constrained system of course. The constraint $0=P^{2}$ , arises for the simplest kind of such actions. Now , This has the trivial 0 solution if all signs are positive or negative. It also has has nontrivial solutions if some of the signs are positive and some are negative. Ghosts will eliminate all but the 1T dimension case. So the question is : Is gauge symmetry really the origin of special relativity on the target space manifold ? That is mathematical consistency chooses just $O(1,n_{+})$ as the only possible target space symmetry "At least locally". If so , does this suggests that it is possible to find consistency conditions that determines the number of spacetime dimensions ? What about symplectic and the other classical groups ?  Also what about the exceptional groups ?

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