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Survey of two-time physics. (English) Zbl 0990.83010
Two-time physics (2T) is a general reformulation of one-time physics (1T) that displays previously unnoticed hidden symmetries in 1T dynamical systems and establishes previously unknown duality-type relations among them. This may play a role in displaying the symmetries and constructing the dynamics of little understood systems, such as M-theory. 2T-physics describes various 1T dynamical systems as different $$d$$-dimensional ‘holographic’ views of the same 2T system in $$d+2$$ dimensions. The ‘holography’ is due to gauge symmetries that tend to reduce the number of effective dimensions. Different 1T evolutions (i.e. different Hamiltonians) emerge from the same 2T-theory when gauge fixing is done with different embeddings of $$d$$ dimensions inside $$d+2$$ dimensions. Thus, in the 2T setting, the distinguished 1T which we call ‘time’ is a gauge-dependent concept. The 2T-action also has a global $$SO(d,2)$$ symmetry in flat spacetime, or a more general $$d+2$$ symmetry in curved spacetime, under which all dimensions are on an equal footing. This symmetry is observable in many 1T-systems, but it remained unknown until discovered in the 2T formalism.

##### MSC:
 83E30 String and superstring theories in gravitational theory 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
##### Keywords:
two-time physics; holography; M-theory; Hamiltonians
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