TFPT scientific source excerpt
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000103 | \begin{definition}[Operational seed category]
000104 | \label{def:operational-seed-category}
000105 | Let $\Seedop$ denote the category whose objects are tuples
000106 | \[
000107 | \mathfrak S=(\mathfrak A_{\mathrm{loc}},\tau_t,\Theta,\omega,[u_\Sigma],\mathcal D_{\mathrm{coll}})
000108 | \]
000109 | satisfying:
000110 | \begin{enumerate}[label=(\roman*), leftmargin=1.5em, topsep=3pt, itemsep=2pt]
000111 |     \item $\mathfrak A_{\mathrm{loc}}$ is a quasilocal Euclidean observable net with positive-time
000112 |     reflection $\Theta$;
000113 |     \item $\omega$ is reflection positive and clustering on the admissible local algebra, with finite
000114 |     relative action with respect to the declared reference sector;
000115 |     \item $[u_\Sigma]\neq 0$ is a nontrivial seam class;
000116 |     \item $\mathcal D_{\mathrm{coll}}$ is a first-order elliptic collar generator whose positive-side
000117 |     restriction is reflection regular.
000118 | \end{enumerate}
000119 | Morphisms are unitary intertwiners preserving the displayed structures.