On the Lorentz Group SO(3,1),Geometrical Supersymmetric Action for Particles and Square-Root OperatorsII. Squeezed States and Relativistic Wave Equations

DIEGO JULIO CIRILO-LOMBARDO

Physics of Particles and Nuclei Letters,

SPRINGER-V D I VERLAG GMBH

Año: 2007 p. 239 - 244

1547-4771

The geometrical relativistic superparticle action is analyzed from the theoretical group point of view. To this end an alternative technique of quantization, outlined by the authors in a previous work and based on the correct interpretation of the square-root Hamiltonian, is used. We show that the obtained spectrum of physical states and the Fock construction in this previous work consist of squeezed states with the even and odd representations with the lowest weights λ = 1/4 and λ= 3/4 corresponding to four possible (nontrivial) fractional representations for the group decomposition of the spin structure. The conserved currents are computed, and a new relativistic wave equation is proposed and explicitly solved for the time-dependent case. The relation between the relativistic Schrödinger equation and the time-dependent harmonic oscillator is analyzed and discussed.