A q-Lorentz Algebra From q-Deformed Harmonic Oscillators

Details A q-Lorentz Algebra From q-Deformed Harmonic Oscillators A q-Lorentz Algebra From q-Deformed Harmonic Oscillators

1995-09-08

arxiv.org/abs/q-alg/9509007v2

Chaos Solitons Fractals 8:823-834,1997

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, REVTeX, uses aps.sty

Scientific paper

10.1016/S0960-0779(96)00159-2

A mapping between the operators of the bosonic oscillator and the Lorentz rotation and boost generators is presented. The analog of this map in the $q$-deformed regime is then applied to $q$-deformed bosonic oscillators to generate a $q$-deformed Lorentz algebra, via an inverse of the standard chiral decomposition. A fundamental representation, and the co-algebra structure, are given, and the generators are reformulated into $q$-deformed rotations and boosts. Finally, a relation between the $q$-boson operators and a basis of $q$-deformed Minkowski coordinates is noted.

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