Abstract
For a sequence of vector states on the Boson Fock space which are norm convergent on the Newton-Wigner local algebras, conditions are given which guarantee norm convergence on the relativistic local algebras also. These conditions are verified for the cutoff physical vacuum states of the P ( ϕ ) 2 P{(\phi )_2} field theory, and yield a simplification of the proof of the locally normal property of the physical vacuum in that theory.
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