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Operator algebra
About: Operator algebra is a research topic. Over the lifetime, 5783 publications have been published within this topic receiving 165303 citations.
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TL;DR: In this paper, the authors study the algebra of Wilson loop and Wilson surface operators and multiplets of ground states on the three-torus, and explicitly calculate the $\mathcal{S}$ and ''Mathcal{T}$ matrices, which encode fractional braiding statistics and the topological spin of looplike excitations, respectively.
Abstract: The multiflavor $\mathit{BF}$ theories in (3+1) dimensions with cubic or quartic coupling are the simplest topological quantum field theories that can describe fractional braiding statistics between looplike topological excitations (three-loop or four-loop braiding statistics). In this paper, by canonically quantizing these theories, we study the algebra of Wilson loop and Wilson surface operators, and multiplets of ground states on the three-torus. In particular, by quantizing these coupled $\mathit{BF}$ theories on the three-torus, we explicitly calculate the $\mathcal{S}$ and $\mathcal{T}$ matrices, which encode fractional braiding statistics and the topological spin of looplike excitations, respectively. In the coupled $\mathit{BF}$ theories with cubic and quartic coupling, the Hopf link and Borromean ring of loop excitations, together with pointlike excitations, form composite particles.
40 citations
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TL;DR: In this article, it was shown that a biseparating map between spaces B(E) and some other Banach algebras, is automatically continuous and an algebra isomorphism.
Abstract: We prove that a biseparating map between spaces B(E), and some other Banach algebras, is automatically continuous and an algebra isomorphism.
40 citations
TL;DR: In this article, the fusion rules of a vertex operator algebra W (0) + R, which is a VOA over the real number field R and has a positive definite invariant bilinear form, were studied.
40 citations
01 Jan 1998
TL;DR: In the recent years, the theory of deformations, mainly in the spirit of quantum groups and quantum algebras, has been the subject of considerable interest in statistical physics as discussed by the authors.
Abstract: In the recent years, the theory of deformations, mainly in the spirit of quantum groups and quantum algebras, has been the subject of considerable interest in statistical physics. More precisely, deformed oscillator algebras have proved to be useful in parasiatistics(connected to irreducible representations, of dimensions greater than 1, of the symmetric group), in anyonic statistics(connected to the braid group) that concerns only particles in (one or) two dimensions, and in q-deformed statisticsthat may concern particles in arbitrary dimensions. In particular, the q-deformed statistics deal with:
(i)
q-bosons (which are bosons obeying a q-deformed Bose-Einstein distribution),
(ii)
q-fermions (which are fermions obeying a q-deformed Fermi-Dirac distribution), and
(iii)
quons (with qsuch that q k = 1, where k∈ ℕ \ {0,1}) which are objects, refered to as k-fermions in this work, interpolating between fermions (corresponding to k= 2) and bosons (corresponding to k→ ∞).
40 citations