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 — preprints:2006:ttp06-29 [2016/03/15 20:39] (current) Line 1: Line 1: + ====== 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. + ​ + |**Hartmut Pilkuhn** ​ | + | {{preprints:​2006:​ttp06-29.pdf|PDF}} {{preprints:​2006:​ttp06-29.ps|PostScript}} ​  | + | |