Group theory of pseudo-oscillators

  title={Group theory of pseudo-oscillators},
  author={Yu. F. Smirnov and A. P. Shustov},
It is shown that O(p,q) and Sp(2,R) are complementary groups in the space of pseudo-oscillator Hpq eigenfunctions. The structure and irreducible representation of both invariancy algebra and generating-spectrum algebra are discussed in detail. It is proved that the transformation brackets between the basis diagonalising the compact generator and the basis diagonalising the non-compact generator in the case of discrete series of irreducible representations of the SU(1,1) group coincide with the… CONTINUE READING