ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract We prove that the λ(ϕ4)2 quantum field theory model is Lorentz covariant, and that the corresponding theory of bounded observables satisfies all the Haag-Kastler axioms. For each Poincaré transformation {a, Λ} and each bounded regionB of Minkowski space we construct a unitary operatorU which correctly transforms the field bilinear forms:Uϕ(x, t)U*=ϕ({a, Λ} (x, t)), for (x, t) ∈B. We also consider the von Neumann algebra $$\mathfrak{A}(B)$$ of local observables, consisting of bounded functions of the field operators ϕ(f)=ε ϕ(x, t)f(x, t)dx dt, suppf ⊂B. We define a *-isomorphism $$\sigma _{\{ a,\Lambda \} } :\mathfrak{A}(B) \to \mathfrak{A}(\{ a,\Lambda \} B)$$ by setting σ{a, Λ}(A)=U A U*. The mapping $$\{ a,\Lambda \} \to \sigma _{\{ a,\Lambda \} } $$ is a representation of the Poincaré group by *-automorphisms of the normed algebra $$ \cup _B \mathfrak{A}(B)$$ of local observables.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01646027
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