Relativistic kinematics kinetic energy

It must be emphasized that these expressions are still exact when compared to the original untransformed operator. The transformed operator /i would be completely decoupled if V = 0, i.e., if the particle were moving freely, and hence only the kinetic energy operator (apart from the rest energy term) remains. Thus, the even terms of the free-particle Foldy-Wouthuysen transformation already account for all so-called kinematic relativistic effects. 

In the traditional approaches to nuclear physics, nuclear structure and nuclear reactions at low energies are studied using nonrelativistic many-body theory. The state of the nucleons is described by a nonrelativistic Hamiltonian, and the interactions are taken to be static potentials which are assumed to arise from meson exchange. The average kinetic energy of a bound nucleon and the nuclear binding potential (in the two-component Pauli representation) are both much less than the nucleon mass, so that, in the traditional approach, neither relativistic kinematics nor dynamics should be needed in descriptions of low energy nuclear phenomena. 

A different relativistic kinematic substitution is used by Arellano et al. [Ar 90a, Ar 90b] and Picklesimer et al. [Pi 84]. They replace the quantity (E - c q- ) with the total relativistic kinetic energy in the projectile-nucleus COM system that is,... 

Relativistic corrections to the ground state energies of many particle systems are expected in two places. First there is the kinematic correction. The non-relativistic kinetic energy has to be replaced by its relativistic equivalent... 

---