Abstract
In this chapter we will investigate C*-dynamical systems {A, ℝd, α}, i.e., systems for which the symmetry group is the d-dimensional translation group. Let ℝ′d be the dual space of ℝd and C′ ⊂ ℝ′d be a proper, closed convex cone with interior points. We want to characterize representations {ℌ, π, U, C′} of the above C*-dynamical system having the properties: (α) π is a non-degenerate representation of A acting on ℌ, (β) U(a), a ∈ ℝd is a continuous unitary representation of the translation group ℝd implementing the automorphisms α a , i.e.,
(γ) The spectrum of U(a) is contained in C′.
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© 1996 Springer-Verlag Berlin Heidelberg
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(1996). Translations and the Spectrum Condition. In: Translation Group and Particle Representations in Quantum Field Theory. Lecture Notes in Physics Monographs, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49954-1_2
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DOI: https://doi.org/10.1007/978-3-540-49954-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61140-0
Online ISBN: 978-3-540-49954-1
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