Manuscript En06-A@1 · En06-A.tex · section · e04c9892

The storage algebra is not yet a dynamical spacetime net

Observable algebras: what commutation actually establishes › The storage algebra is not yet a dynamical spacetime net · lines 1871–1887

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For a nested family, let

Λ_{\infty} = n ⋃ Λ_{n}, R_{\infty} = Λ_{\infty} \times N, B_{\infty} = ρ \in R_{\infty} ⨂ M_{2} .

The tensor product is the quasi-local inductive limit over finite register sets BratteliRobinson. The inclusions of the scale storage algebras are unital $*$ -monomorphisms. This is a valid algebraic construction.

It does not identify Heisenberg observables at different scales, or prove that moving report effects have norm limits.

Displayed formulas in this passage

unlabeled · line 1874
$Λ_{\infty} = n ⋃ Λ_{n}, R_{\infty} = Λ_{\infty} \times N, B_{\infty} = ρ \in R_{\infty} ⨂ M_{2} .$

Nearby in this section

example: Example: Constant laws without norm convergence
remark: Remark: Kraus operators are not intrinsic observables