N-Body Relativistic C. M. Variables and the Two-Body Interacting System

劉明昆(M. K. Liou)

《Chinese Journal of Physics》 15卷4期 (1977/12) Pp. 286-305

並列摘要

The general unitary operator to be used in transforming the nonrelativistic c. m. dynamical variables to the relativistic c. m. dynamical variables is constructed and its properties are discussed. The constructed operator is correct to all orders in mass-r and contains an arbitrary function of internal variables. Because of this arbitrary function, we find that there is an arbitrariness in the choice of the c. m. variables. We also find that this arbitrary function represents the internal interaction when it does not commute with the total mass operator of the system. Thus we obtain a general method of introducing an internal interaction into the relativistic system. Many well-known Hamiltonians introduced by Bakamjian and Thomas, Foldy, and Sudarshan are reproduced. Two different sets of nonrelativistic variables are discussed and the mathematical relation between them is obtained.