The Equation of Motion of a Spinning Particle in a Meson Field

R. C. Majumdar, S. P. Pandya, S. Gupta
1952 Progress of theoretical physics  
The divergence difficulties associated with the selfforce in a field theory, recently led Wheeler and Feynman 1 ) to revive the theory of "Action at a distance ", previously studied by Fokker and others. By incorporating in it the conception of "complete absorption" they succeeded in obtaining the equation of motion. of a point particle in an electromagnetic field, which described the reaction of the radiation correctly. Kanazawa2) and Havas3) have extended Wheeler and Feynman's theory to
more » ... the equation of motion of a nucleon having a mesic charge. We shall in the present note further develop the theory to obtain the equations of motion of a spinning particle, with spin moment 9 moving in a neutral meson field. We start with the variation principle which, for vector meson field, makes the action given by at extremum. Here the metric tensor 9r<" is taken as 900 = -911 = -922= -933=1, and the velocity of light c=l; Tj, Zj~, and Sif."' denote respectively. the proper time, the coordinates and spin of the particle "i" and T j is the angular momentum tensor. G(s) is the Green's function satisfying the equation, where M=rest mass of meson. (3) We define and Gkf . ' ' 11 (x) = a¢k'll (x) ;aXf.'-a¢kP.(X) ;ax". Now giving a small rotation IJ,fJar", to particle " "" and remembering (6) we obtain the equations of motion after applying· the condition of" complete absorption ", and Sf."'v" =0, The minus sign after the square bracket denotes that the terms inside the bracket with p. and" interchanged are to be subtracted and the dots indicate differentiation with respect to the proper time. We have used the abbreviation The equations obeyed by the potentials and the field strengths are easily obtained from· (2), (4) and (5) ; and (9)
doi:10.1143/ptp.8.670 fatcat:4dpdwoze5bfvdo32johol5y4ee