I found a book on the interesting and very difficult topic of many-body classical relativistic theory

Classical Relativistic Many-Body Dynamics

Trump, M.A., Schieve, W.C
Springer, Fundamental Theories of Physics, Vol. 103

This relativistic covariant many-body formulation overcomes the no go theorem by Jordan and Sudarshan [1] by giving up the locality of the interactions and the individual mass-shell conditions. These are not simply cosmetic upgrades but have serious consequences on how we should understand classical physics.

"The single particle has no significance; it is the whole system that counts" --Lanczos


[1] FROM CLASSICAL TO
QUANTUM MECHANICS
Giampiero Esposito, Giuseppe Marmo