Local Observables in $\operatorname{SU}_q(2)$ Lattice Gauge Theory
| Autor: | Bonzom, Valentin, Dupuis, Maïté, Girelli, Florian, Pan, Qiaoyin |
|---|---|
| Přispěvatelé: | HEP, INSPIRE |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
High Energy Physics - Theory
spinor: operator algebra: Poisson High Energy Physics::Lattice High Energy Physics - Lattice (hep-lat) lattice field theory deformation FOS: Physical sciences [PHYS.HLAT] Physics [physics]/High Energy Physics - Lattice [hep-lat] Mathematical Physics (math-ph) [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph] Heisenberg Wilson loop phase space High Energy Physics - Lattice High Energy Physics - Theory (hep-th) [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th] model: topological quantization quantum gravity: loop space Mathematical Physics lattice |
| Popis: | We consider a deformation of 3D lattice gauge theory in the canonical picture, first classically, based on the Heisenberg double of $\operatorname{SU}(2)$, then at the quantum level. We show that classical spinors can be used to define a fundamental set of local observables. They are invariant quantities which live on the vertices of the lattice and are labelled by pairs of incident edges. Any function on the classical phase space, e.g. Wilson loops, can be rewritten in terms of these observables. At the quantum level, we show that spinors become spinor operators. The quantization of the local observables then requires the use of the quantum $\mathcal{R}$-matrix which we prove to be equivalent to a specific parallel transport around the vertex. We provide the algebra of the local observables, as a Poisson algebra classically, then as a $q$-deformation of $\mathfrak{so}^*(2n)$ at the quantum level. This formalism can be relevant to any theory relying on lattice gauge theory techniques such as topological models, loop quantum gravity or of course lattice gauge theory itself. 36+4 pages, 9 figures; updated version submitted to journal |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|