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Comments on a recent solution to Wightman’s axioms. (English) Zbl 0892.46085
Summary: A class of exact Wightman functionals satisfying all fundamental physical requirements in an arbitrary number of space-time dimensions, which bear the appearance of describing interacting fields, was recently constructed by C. Read [Commun. Math. Phys. 177, No. 3, 631-671 (1996; Zbl 0851.46051)]. It is shown here that the construction can be considerably generalized and that even the enlarged class belongs to the Borchers class of a system of generalized free fields.

MSC:
46N50 Applications of functional analysis in quantum physics
81T05 Axiomatic quantum field theory; operator algebras
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[1] Read, C. J.: Quantum field theories in all dimensions. Univ. Cambridge (UK) preprint (1994), to appear in Commun. Math. Phys. · Zbl 0851.46051
[2] Streater, R. F., Wightman, A. S.: PCT, Spin and Statistics, and All That. New York-Amsterdam: W. A. Benjamin, 1964 For a profound guide to more recent achievements of the theory see also: Streater, R. F.: Outline of axiomatic relativistic quantum field theory. Rep. Progr. Phys.38, 771–846 (1975), especially Chapter 3
[3] Greenberg, O. W.: Generalized free fields and models of local field theory. Ann. Phys. (N.Y.)16, 158–176 (1961) · Zbl 0099.23103
[4] Borchers, H.-J.: Algebraic aspects of Wightman field theory. In: R. N. Sen and C. Weil (eds.), Statistical Mechanics and Field Theory, Haifa Lectures 1971; New York: Halstedt Press, 1972 · Zbl 0321.46058
[5] Borchers, H.-J.: Über die Mannigfaltigkeit der interpolierenden Felder zu einer kausalenS-Matrix. Nuovo Cim.15, 784–794 (1960) · Zbl 0093.44002
[6] Licht, A. L.: A generalized asymptotic condition. Ann. Phys. (N.Y.)34, 161–186 (1965) · Zbl 0128.45802
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