= Time-slice axiom
The <time-slice axiom> says that an algebra generated in an arbitrarily thin suitable neighbourhood of a Cauchy surface generates the algebra of its causal development. For $O$ such a neighbourhood in its development $D(O)$, this is $\mathcal A(O)=\mathcal A(D(O))$. Precise global and local versions can differ in the regions to which they apply. For a local hyperbolic field equation, later fields can be represented using the initial field and its conjugate momentum in the corresponding <domain of dependence>.
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