A Note About "Analyzing Photon-Electron Interaction by Quantum Matrix Approach"

Abstract



In an earlier article “Analyzing Photon-Electron Interaction by Quantum Matrix Approach”,¹ the emission amplitude of photon is derived in relation to the formulation of bare electron’s self-energy process. However the dimensionality in that paper was not explained sufficiently. Emphasizing the linkage between the emission amplitude and the notion of probability density embodied in the system’s wavefunction is quite natural and analysis indicates that an approximation may be obtained by focusing on a double- photon state whose wavefunction is (2^1/2Λ₂²k₁k₂)^-1h(k₁)h(k₂)[d^1/2(k₁-p)|k₁,k₂>+[d^1/2(k₂-p)|k₂,k₁>]. Delta function here is to indicate the energy of emitted photon is equivalent to incoming one in the mass-center frame while the other photon’s energy can alter within the range. Hence the energy dependent formula can be corrected as L₀(q) = q{m(1+2q)^1/2[(1+2q)^1/2-1]²}^-1 with q being a division between the incoming photon momentum and the electron mass (natural units). If initially electron is at rest in the laboratory frame, the amplitude in this frame is L(q, α’)= q(1+2q)^1/2{m^1/2[(1+2q)^1/2-1](1 + q – qcosα’)}^-2 where α’ is the angle between the emitted photon and the symmetric axis of laboratory frame. L₀ and L are interrelated to each other with the aid of differential solid angle. The electric interaction mediated by neutrino-antineutrino has not been discussed in detail in this article.



Reference

1. William Lee, k17.00018, APS April Meeting 2022, New York.