Separable Four-dimensional Harmonic Oscillators and Representations of the Poincar\'e Group
Kim, Y. S.
arXiv, 9811013 / Harvested from arXiv
Text on arXiv
It is possible to construct representations of the Lorentz group using four-dimensional harmonic oscillators. This allows us to construct three-dimensional wave functions with the usual rotational symmetry for space-like coordinates and one-dimensional wave function for time-like coordinate. It is then possible to construct a representation of the Poincar\'e group for a massive particles having the O(3) internal space-time symmetry in its rest frame. This oscillator can also be separated into two transverse components and the two-dimensional world of the longitudinal and time-like coordinates. The transverse components remain unchanged under Lorentz boosts, while it is possible to construct the squeeze representation of the $O(1,1)$ group in the space of the longitudinal and time-like coordinates. While the squeeze representation forms the basic language for squeezed states of light, it can be combined with the transverse components to form the representation of the Poincar\`e group for relativistic extended particles.
Publié le : 1998-11-16
Classification:  Mathematical Physics,  High Energy Physics - Phenomenology,  High Energy Physics - Theory,  Quantum Physics 
@article{9811013,
     author = {Kim, Y. S.},
     title = {Separable Four-dimensional Harmonic Oscillators and Representations of
  the Poincar\'e Group},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9811013}
}

Kim, Y. S. Separable Four-dimensional Harmonic Oscillators and Representations of
  the Poincar\'e Group. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9811013/