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— | preprints:2006:ttp06-29 [2016/03/15 20:39] (current) – created - external edit 127.0.0.1 |
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| ====== TTP06-29 Equations for Relativistic Particles, Binaries and Ternaries ====== |
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| <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}} | |
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