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We describe how to define observables analogous to quantum fields for the semicontinuous limit recently introduced by Jones in the study of unitary representations of Thompsons groups $F$ and $T$. We find that, in terms of correlation functions of these fields, one can deduce quantities resembling the conformal data, i.e., primary fields, scaling dimensions, and the operator product expansion. Examples coming from quantum spin systems and anyon chains built on the trivalent category $mathit{SO}(3)_q$ are studied.
There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way. Moreover, they are
$CPT$ groups of higher spin fields are defined in the framework of automorphism groups of Clifford algebras associated with the complex representations of the proper orthochronous Lorentz group. Higher spin fields are understood as the fields on the
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the Hermitian str
The paper recalls and point to the origin of the transformation laws of the components of classical and quantum fields. They are considered from the standard and fibre bundle point of view. The results are applied to the derivation of the Heisenberg
Relying on the main results of [Guralnick-Tiep], we classify all unitary $t$-groups for $t geq 2$ in any dimension $d geq 2$. We also show that there is essentially a unique unitary $4$-group, which is also a unitary $5$-group, but not a unitary $t$-group for any $t geq 6$.