By H. Murihead (Auth.)
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Only the spatial coordinate x± and time coordinate x 4 can be affected by this motion. Therefore any transformation between the coordinate frames can only link χγ and ;v4 with x'± and x'4. , cos 0 = V(! - 02) FIG. = 7, sin 0 = ißy. 2. 13) may be extended to four vectors. 14) A2 = A'2 A3 = A'3 Α4 = γ(ίβΑ[ + A$. 16) where the symbols E and ρ refer to total energy and charge density respectively. 14) shows that the sum of the products of the equivalent components of two four-vectors, ΑλΒλ, is a scalar quantity and is the four-dimensional equivalent of the normal scalar product of two vectors.
3. 58) where ηλ is a unit vector normal to the element of area of the hypersurface. This definition is illustrated in Fig. 3. For example we may write do4 = — «4 dxi dx2 dx3 = — n^dxdy dz = — tf4 dx. 3] RELATIVISTIC WAVE EQUATIONS 53 The element of four-dimensional volume is represented as d*x = — dx± dx2 dx3 dx± = dxdt. 61) The term 1 // again appears because of the definition xA = ict ; if a coordinate scale with real fourth component is used the i can be dropped. 63) i φ j φ k can be constructed for four-dimensional systems.
We will therefore represent the cross-section for the process i - > / a s -Sr = T; &, w 4 Σ Σ i^i2· W A Σ Σ l^/l2· (2·8) dQ (2sa + 1) (2sb + 1) pc i « Now consider the reverse process/-» i. 9) and if we represent the π+d and pp systems as/and i respectively * - = 2 υ . ( 2 , , + 1)*£2. 2 where we have inserted the factor (2se + 1) = 3 for the deuteron and (2sa + 1) = 2 for the proton. 11) where the symbol oT represents the total cross-section. The factor 2 appears because the two protons are indistinguishable.