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Extended noncommutative Minkowski spacetimes and hybrid gauge symmetries. (arXiv:1805.07099v2 [hep-th] CROSS LISTED)
来源于:arXiv
We study the Lie bialgebra structures that can be built on the
one-dimensional central extension of the Poincar\'e and (A)dS algebras in (1+1)
dimensions. These central extensions admit more than one interpretation, but
the simplest one is that they describe the symmetries of (the noncommutative
deformation of) an Abelian gauge theory, $U(1)$ or $SO(2)$ on the (1+1)
dimensional Minkowski or (A)dS spacetime. We show that this highlights the
possibility that the algebra of functions on the gauge bundle becomes
noncommutative. This is a new way in which the Coleman-Mandula theorem could be
circumvented by noncommutative structures, and it is related to a mixing of
spacetime and gauge symmetry generators when they act on tensor-product states.
We obtain all Lie bialgebra structures on centrally-extended Poincar\'e and
(A)dS which are coisotropic w.r.t. the Lorentz algebra, and therefore all of
them admit the construction of a noncommutative principal gauge bundle on a
quantum homogeneous M 查看全文>>