REPRESENTATIONS AND PROPERTIES OF PARA-BOSE OSCILLATOR OPERATORS .1. ENERGY POSITION AND MOMENTUM EIGENSTATES

Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation script Dsignα of the para-Bose system is obtained as the direct sum Dβ⊕D β+1/2 of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation script D signα, using the matrix mechanical method. The orthogonality, completeness, and the overlap of diese eigenstates are derived. The momentum eigenstates are also derived using the wave mechanical method by specifying the domain of the definition of the momentum operator in addition to giving it a formal differential expression. By a careful consideration in this manner we find that the two apparently different solutions obtained by Ohnuki and Kamefuchi in this context are actually unitarily equivalent. © 1980 American Institute of Physics.