Review of the Perspective

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In quantum physics just as in classical physics the concept of “field” serves to implement the principle of locality. In particular, a “quantum field” should not be regarded as being more or less synonymous with a “species of particles”. While it is true that with each type of particle we may associate an “incoming field” and an “outgoing field”, these free fields are just convenient artifacts and the discussion of collision theory in Chapter II, sections 3 and 4 should make it clear that the primary physical interpretation of the theory is given in terms of local operations, not in terms of particles. Specifically, we have used the basic fields to associate to each open region 𝒪 in space-time an algebra 𝒜(𝒪) of operators on Hilbert space, the algebra generated by all Φ(ƒ), the fields “smeared out” with test functions ƒ having their support in the region 𝒪. We have interpreted the elements of 𝒜(𝒪) as representing physical operations performable within 𝒪 and we have seen that this interpretation tells us how to compute collision cross sections once the correspondence $${\cal O}\rightarrow {\cal A}({\cal O})$$ (III.1.1) is known.