Boson Quantum Field Models
The local algebras, as constructed in Section 8, are not acting on the Hilbert space of physical particles. On the physical Hilbert space, as in the laboratory, the states have a simple asymptotic description for large values of |t|. One observes isolated particles or clusters formed as bound states of several elementary particles. Because they are widely separated, the elementary particles or bound states do not interact, and they behave asymptotically like free particles. We present here the functional analysis preparation for the construction of the physical Hilbert space ℱren in Section 10. On ℱren, the above asymptotic description of the states should be valid. We begin by listing without proof three general results. A state on a C*-algebra is by definition a positive linear functional ω which satisfies the normalization condition ω(I) = 1.
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