nLab
time slice axiom

Idea

In quantum field theory the time slice axiom is an additional axiom often considered on top of the basic Haag-Kastler axioms: it encodes the property that the time evolution of the classical field theory underlying a QFT is governed by well-defined initial value problems.

Definition

A local net of observables $A:\mathrm{Op}(X)\to C^{*}\mathrm{Alg}$ satisfies the time slice axiom if whenever a causal inclusion of Lorentzian spaces $O_1\hookrightarrow O_2$ is such that $O_1$ contains a Cauchy surface of $O_2$ then $A(O_1\hookrightarrow O_2)$ is an isomorphism.