Explicit representations of a single para-Bose operator

G. N. Brodimas, A. D. Jannussis, D. Sourlas +2 more

K. V. Kademova

Thomas F. Jordan, Narasimhaiengar Mukunda, Stephen V. Pepper

All of the irreducible representations are found for a single pair of creation and annihilation operators which together with the symmetric or antisymmetric number operator satisfy the generalized commutation relation characteristic of para-Bose or para-Fermi field quantization. The procedure is simply to identify certain combinations of these three operators with the three generators of the three-dimensional rotation group in the para-Fermi case, and with the three generators of the three-dimensional Lorentz group in the para-Bose case. The irreducible representations are then easily obtained by the usual raising and lowering operator techniques. The applicability of these techniques is demonstrated by a simple argument which shows that the commutation relations require that the generator to be diagonalized have a discrete spectrum.

Manfred Schmutz

A set of n para-Bose operators of order p is explicitly constructed in terms of n×p Bose operators.

J. K. Sharma, C. L. Mehta, Narasimhaiengar Mukunda +1 more

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ‖z;α〉 defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ‖z;α〉〈z;α‖ and the other containing the pseudodiagonal basis ‖z;α〉〈−z;α‖. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible α dependence of this minimum value is considered.