# Notes on Elementary Particle Physics by H. Muirhead

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4) If we write Ee = ηΔ the above equation becomes (2π) 5 r„ J V A2 mejA This equation can be easily evaluated in the limit mJA -> 0, yielding 1 2 5 Γ„ = -L = - ^ L (4π) zi f άηη\\ -η)2 5 r„ (2π) J 0 5 G2

Thus the normal spin operators can be regarded as non-relativistic extensions of Γσ. 5) and since Γ2α is Lorentz invariant, this eigenvalue remains the same in any reference frame. In the rest frame of the particle Γ = mS Γ 4 = 0. Now consider the situation when m -> 0 we then have Γ σ 2 ->0 But we also have Ρ σ 2 ->0 for m - > 0 . ) 44 RELATIVISTIC WAVE EQUATIONS AND FIELDS [Ch. 3 and so rs. = o. This is a Lorentz invariant expression and must hold in all reference frames, even when ß -» 1 which is equivalent to saying m -> 0.

This enormous discrepancy arises from the neglect of \Mfi\2. Before we con­ sider matrix elements in detail, however, the problems of the next chapter must be satisfactorily settled. 2(c). R - E CHAPTER 3 RELATIVISTA WAVE EQUATIONS AND FIELDS IN ORDER to produce satisfactory matrix elements we must firstly produce satisfactory descriptions of particle states. These must patently be relativistic because 1. most of elementary particle physics is concerned with particles moving with velocities ß (= v/c) in the limit ß -> 1 ; 2.