= Spectrum condition
{title2=$\operatorname{Sp}(P)\subseteq\overline V_+$}
In a translation-covariant quantum field theory on Minkowski spacetime, the joint spectrum of the energy-momentum generators is required to lie in the closed future light cone. With signature $(+,-,-,-)$ this means $p^0\ge0$ and $p^2\ge0$. The <spectrum condition> implements a positive-energy stability requirement in every inertial frame. It constrains the Fourier support and analyticity of vacuum correlation functions but does not by itself assert spacelike commutation or an initial-value property.
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