On the quantization of the superparticle action in proper time and the Lorentz group SO(3,1),

DIEGO JULIO CIRILO-LOMBARDO

Prague, Czech Republic

Conferencia; 8th International Conference on Path Integrals from Quantum Information to Cosmology,; 2005

In this work the problem of the square root operator is analyzed. To this end weconsidered a relativistic geometrical action of a particle in the superspace in order toquantize it and to obtain the spectrum of physical states but remaind the Hamiltonianin the natural square root form. We show, after complete quantization of the model,that the physical states that the square root Hamiltonian can operate correspond to therepresentations with the lowest weights s = 1/4 and s = 3/4 .