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Reference6 articles.
1. For a proof of Von Neumann theorem see e.g. [SNS 96]. For the characterization of the Fock representation in terms of existence of the number operator, see G.F. Dell’Antonio and S. Doplicher, J. Math. Phys. 8, 663 (1967);
2. J.M. Chaiken, Comm. Math. Phys. 8, 164 (1967);
3. Ann. Phys.42, 23 (1968) and references therein.
4. See e.g. O. Bratteli and D.K. Robinson, Operator Algebras and Quantum Statistical Mechanics, Vol. 2, Springer 1996, Sect. 5.2.3; see also [SNS 96].
5. H.J. Borchers, R. Haag and B. Schroer, Nuovo Cim. 29, 148 (1963). For a general look at free fields from the point of view of representations of the algebra of canonical variables (canonical quantization), see A.S. Wightman and S. Schweber, Phys. Rev. 98, 812 (1955);