A Note on Angular Momentum Commutators in Light-Cone Formulation of Open Bosonic String Theory

Details A Note on Angular Momentum Commutators in Light-Cone Formulation of Open Bosonic String Theory A Note on Angular Momentum Commutators in Light-Cone Formulation of Open Bosonic String Theory

2011-04-22

arxiv.org/abs/1104.4446v2

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX. v2: Various pedagogical improvements

Scientific paper

We recalculate in a systematic and pedagogical way one of the most important results of Bosonic open string theory in the light-cone formulation, namely the [J^{-i},J^{-j}] commutators, which together with Lorentz covariance, famously yield the critical dimension D=26 and the normal order constant a=1. We use traditional transverse oscillator mode expansions (avoiding the elegant but more advanced language of operator product expansions). We streamline the proof by introducing a novel bookkeeping/regularization parameter \kappa to avoid splitting into creation and annihilation parts, and to avoid sandwiching between bras and kets.

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