|XXXVII Workshop on Geometric Methods in Physics||1-7.07.2018|
|VII School on Geometry and Physics||25-29.06.2018|
Observational consequences of light-like deformations of the Poincaré algebra from (extended) jordanian twist.
In the talk I discuss the observational consequences of the light-like deformations of the Poincaré algebra induced by the jordanian and the extended jordanian classes of Drinfel'd twists. We consider four type of deformations, obtained from the twists and their “flipped” versions. In two of the cases the set of the deformed operators include a subalgebra of pseudo-hermitian operators, conserving (pseudo) hermiticity in the positive light-cone direction but not for all negative light-cone operators.
Twist-deformed generators belonging to a universal enveloping algebra close non-linear $W$-algebras. In one of the cases the $W$-algebra is responsible for the existence of bounded domains of the deformed momenta. The Hopf algebra coproduct implies associative non-linear additivity of the multi-particle states. One can observe a parallel with the limit on velocity and additive velocity formula in special relativity.
A subalgebra of twist-deformed observables is recovered whenever the twist-deformed generators are either hermitian or pseudo-hermitian with respect to a common invertible hermitian operator.
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