 Segal (1959, p. 5) was the first to suggest that the beauty and power of the algebraic approach becomes evident when working with an infinite quantum system . The key advantage of the algebraic approach, according to Segal (1959, pp. 5–6), is that one may work in the abstract algebraic setting where it is possible to obtain interacting fields from free fields by an automorphism on the algebra, one that need not be unitarily implementable. Segal notes (1959, p. 6) that von Neumann (1937) had a similar idea (that field dynamics are to be expressed as an automorphism on the algebra) in an unpublished manuscript. Segal notes this advantage in response to a result obtained by Haag (1955), that field theory representations of free fields are unitarily inequivalent to representations of interacting fields. Haag mentions that von Neumann (1938) first discovered ‘different’ (unitarily inequivalent) representations much earlier. A different way of approaching unitarily equivalent representations, by contrast with Segal’s approach, was later presented by Haag and Kastler (1964), who argued that unitarilty inequivalent representations are physically equivalent. Their notion of physical equivalence was based on Fell’s mathematical idea of weak equivalence (Fell 1960).