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preprints:2006:ttp06-29 [2016/03/15 20:39] (current)
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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}} ​  | 
 +| |