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0' satisfies the same V equation as the differential coefficients of X and this matrix S is defined now being with respect to x' instead by V where L,^^ are the elements of the matrix L. We shall continue this discussion in the chapter III, section 4. 1 Here(5y«y = /t4=v,(5ii = <522 = 533 = — ],<544 = 1. This should be distinguished from 5,-j in (52). ELEMENTARY PARTICLES AND COSMIC RAYS 24 Solutions of the Dirac equation for a free particle From now on we for a free particle ^ will confine ourselves to the solutions of the Dirac equation , {p ^ — m)y)=^0.

We shall in the next few chapters be concerned only with single particle wave functions and the concept of interaction as introduced through the perturbation theory. Besides introducing attributes like spin and isotopic spin in the wave function one important mathematical requirement will be imposed, viz. the equations of description involving an operator calculus SINGLE PARTICLE WAVE FUNCTIONS motion should be co variant under Lorentz transformations. This 13 is also physically reasonable since the laws of physics should be describable in the same manner in all inertial frames of reference.

Of the photon therefrom. In this procedure momentum Schrodinger equation of the photon in The Maxwell field and magnetic vectors is space completely specified by the distribution of the electric in space and time. These vectors E{x, t) and H(x, t) satisfy the coupled equations cur\E= divif=0 dt ^^^ 3E curlH=-— divE = 0. e. div J5= 0) with a radiation field and thus only with photons. we tare dealing Taking the Fourier transforms^ of E(x) andH(ap) E{k)=:-^jE{x)e-^''-d^x; we can = -i[k k'E{k) = 0, Further we see that H{k) ^ E{k) and jar (fe) defined by H{k)=^-^JH{x)e-^^-A^x, write the Maxwell's equations in H{k) sis X E{k)], momentum E{k) = i[k space as x H{k)] k'H{k)^0.