# Differences

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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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