====== TTP06-29 Equations for Relativistic Particles, Binaries and Ternaries ======
 
 
<hidden TTP06-29  Equations for Relativistic Particles, Binaries and Ternaries > Relativistic differential equations for bound states of $n$ Dirac
 particles ($n=1,2,3$) are put into forms that depend only on the
 square of the total cms energy. Instead of coupling $4^n$ Dirac components,
 they decompose into two equivalent equations for $4^n/2$ components $\psi$ 
 and $\chi$
 of total chiralities $+1$ and $-1$, respectively. Their time-dependent
 versions are of the Klein-Gordon type; they
 reproduce the relativistic kinematics for the emission of photons or pions.
 Although the equations are presently extended to mesons and baryons within
 perturbative QCD only, the necessity of free Klein-Gordon equations for closed
 systems implies $E^2$-spectra not only for mesons, but also for baryons.
 For binaries, there exists an intricate transformation which turns the
 equation for $\psi$ into an effective one-body Dirac equation. The
 corresponding transformation for $\chi$ is derived here.
 </hidden>
|**Hartmut Pilkuhn**  | 
| {{preprints:2006:ttp06-29.pdf|PDF}} {{preprints:2006:ttp06-29.ps|PostScript}}   |
| |