Bob S said:Do you mean the Fourier transform approach in Section 39 β on page 179? I have some cryptic notes (in my handwriting) in the margin that I cannot decipher anymore.
Bob S
The Breit equation in position space is a relativistic equation that describes the motion of a charged particle in an external electromagnetic field. It takes into account both the electric and magnetic interactions between the particle and the field.
The Pauli approximation is a simplification used in the derivation of the Breit equation. It assumes that the external field is weak, and that the particle's velocity is much smaller than the speed of light. This allows for a more manageable mathematical approach to solving the equation.
The Breit equation can be derived using the Dirac equation, which describes the motion of a relativistic particle. By applying the Pauli approximation and using the position space representation of the Dirac equation, one can arrive at the Breit equation in position space.
The Breit equation in position space has various applications in theoretical physics, such as in the study of atomic and molecular structure, and in the calculation of scattering amplitudes in high-energy physics. It is also used in the development of quantum field theories.
Like any mathematical model, the Breit equation in position space has its limitations. It does not take into account certain effects, such as quantum electrodynamics corrections, and is not applicable to particles with spin greater than 1/2. Additionally, it can only be used for non-relativistic particles.