Higher Dimensional Unitary Braid Matrices: Construction, Associated Structures and Entanglements

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dc.creatorAbdesselam, B.
dc.creatorChakrabarti, A.
dc.creatorDobrev, V. K.
dc.creatorMihov, S. G.
dc.date2007-02-07
dc.date2007-04-09
dc.date.accessioned2026-07-07T10:38:20Z
dc.date.available2026-07-07T10:38:20Z
dc.descriptionWe construct $(2n)^2\times (2n)^2$ unitary braid matrices $\hat{R}$ for $n\geq 2$ generalizing the class known for $n=1$. A set of $(2n)\times (2n)$ matrices $(I,J,K,L)$ are defined. $\hat{R}$ is expressed in terms of their tensor products (such as $K\otimes J$), leading to a canonical formulation for all $n$. Complex projectors $P_{\pm}$ provide a basis for our real, unitary $\hat{R}$. Baxterization is obtained. Diagonalizations and block-diagonalizations are presented. The loss of braid property when $\hat{R}$ $(n>1)$ is block-diagonalized in terms of $\hat{R}$ $(n=1)$ is pointed out and explained. For odd dimension $(2n+1)^2\times (2n+1)^2$, a previously constructed braid matrix is complexified to obtain unitarity. $\hat{R}\mathrm{LL}$- and $\hat{R}\mathrm{TT}$-algebras, chain Hamiltonians, potentials for factorizable $S$-matrices, complex non-commutative spaces are all studied briefly in the context of our unitary braid matrices. Turaev construction of link invariants is formulated for our case. We conclude with comments concerning entanglements.
dc.description26 pages, 1 figure, Addendum and new references are added. To appear in Journal of Mathematical Physics
dc.identifierhttps://arxiv.org/abs/math/0702188
dc.identifierhttp://arxiv.org/abs/math/0702188
dc.identifierJ.Math.Phys.48:053508,2007
dc.identifierdoi:10.1063/1.2737266
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/180683
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Physics
dc.titleHigher Dimensional Unitary Braid Matrices: Construction, Associated Structures and Entanglements
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