Particle Actions in the Superspace, Square Root Operators and Quartions

DIEGO JULIO CIRILO-LOMBARDO

ROMANIAN JOURNAL OF PHYSICS

EDITURA ACAD ROMANE

Año: 2005 p. 875 - 887

1221-146X

In this work the physical and mathematical interpretation of the square root quantum operators is analyzed from the point of view of the theoretical group. To this end, we considered the relativistic geometrical action of a particle in the superspace in order to quantize it and to obtain the spectrum of physical states with the Hamiltonian remaining in the natural square root form. The generators of the group SO(3,1) are introduced and the quantization of this model is performed completely. The obtained spectrum of physical states, with the Hamiltonian operator in square root form, is compared with the spectrum obtained with the Hamiltonian in the standard form (i.e: quadratic in momenta). We show that the only states that the square root Hamiltonian can operate correspond to the representations with the lowest weights ë = 1/4,3/4 lowest weights ë = 1/4,3/4 lowest weights ë = 1/4,3/4 lowest weights ë = 1/4,3/4i.e: quadratic in momenta). We show that the only states that the square root Hamiltonian can operate correspond to the representations with the lowest weights ë = 1/4,3/4 lowest weights ë = 1/4,3/4 lowest weights ë = 1/4,3/4 lowest weights ë = 1/4,3/4