Authors: Kaare Borchsenius
Publish Date: 2015/05/09
Volume: 26, Issue: 1, Pages: 53-69
Abstract
We resolve the spacetime canonical variables of the relativistic point particle into inner products of Weyl spinors with components in a Clifford algebra and find that these spinors themselves form a canonical system with generalized Poisson brackets For N particles the inner products of their Clifford coordinates and momenta form two N × N Hermitian matrices X and P which transform under a UN symmetry in the generating algebra This is used as a starting point for defining matrix mechanics for a point particle in Clifford space Next we consider the string The Lorentz metric induces a metric and a scalar on the world sheet which we represent by a Jackiw–Teitelboim term in the action The string is described by a polymomenta canonical system and we find the wave solutions to the classical equations of motion for a flat world sheet Finally we show that the SL2mathbbC charge and spacetime momentum of the quantized string satisfy the Poincaré algebra
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