Separable Four-dimensional Harmonic Oscillators and Representations of the Poincaré Group

Physics – Mathematical Physics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

LaTex 10 pages, no figures, presented at the 3rd International Workshop on Classical and Quantum Integrable Systems (Yerevan,

Scientific paper

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.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Separable Four-dimensional Harmonic Oscillators and Representations of the Poincaré Group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Separable Four-dimensional Harmonic Oscillators and Representations of the Poincaré Group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Separable Four-dimensional Harmonic Oscillators and Representations of the Poincaré Group will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-615598

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.