### Nonlinear transforms of momenta and Planck scale limitNonlinear transforms of momenta and Planck scale limit

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 Author Chakrabarti, A. Source arXiv.org Content type Text File Format PDF Date of Submission 2002-11-22 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Physics Subject Keyword High Energy Physics - Theory ♦ General Relativity and Quantum Cosmology ♦ physics:gr-qc ♦ physics:hep-th Abstract Starting with the generators of the Poincar\'e group for arbitrary mass (m) and spin (s) a nonunitary transformation is implemented to obtain momenta with an absolute Planck scale limit. In the rest frame (for $m>0$) the transformed energy coincides with the standard one, both being $m$. As the latter tends to infinity under Lorentz transformations the former tends to a finite upper limit $m\coth(lm) = l^{-1}+ O(l)$ where $l$ is the Planck length and the mass-dependent nonleading terms vanish exactly for zero rest mass.The invariant $m^{2}$ is conserved for the transformed momenta. The speed of light continues to be the absolute scale for velocities. We study various aspects of the kinematics in which two absolute scales have been introduced in this specific fashion. Precession of polarization and transformed position operators are among them. A deformation of the Poincar\'e algebra to the SO(4,1) deSitter one permits the implementation of our transformation in the latter case. A supersymmetric extension of the Poincar\'e algebra is also studied in this context. Description Reference: J.Math.Phys. 44 (2003) 3800-3808 Educational Use Research Learning Resource Type Article Page Count 10