Abstract
It is shown that a translationally invariant algebra\(\mathfrak{A}\) of local observables (see [1]) admits a representation in a Hilbert space having a vacuum state. Furthermore an algebraic criterion is given which is necessary and sufficient for the existence of at least one representation of\(\mathfrak{A}\) in which the usual spectral condition for the energy-momentum operators holds.
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Doplicher, S. An algebraic spectrum condition. Commun.Math. Phys. 1, 1–5 (1965). https://doi.org/10.1007/BF01649586
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DOI: https://doi.org/10.1007/BF01649586