7. Relativity and Cosmology

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Setup

\(Clear["Global`*"]; 
Off[General::spell]; 
Off[General::spell1]; 
    \)

Needs["Calculus`VectorAnalysis`"]

Needs["Graphics`PlotField3D`"]

<< "D:\Mma\Inits\ch7init.m"

Clear["Global`*"];

7.2 Problems

7.2.1  Special Relativity Problems

Problem 1:  Decay of a particle

A particle of mass m1 at rest decays into two particles with masses m2 and m3.  The four-momentum of the particle of mass m3 is p3.

Part (a)    Use the scalar invariant m3^2=p3.η.p3 to find the kinetic energy of the particle with mass m2.

\(momRule\  = 
      \ {p1\  -> \ m1\ \ \ \ \ \ \ {1, 0, 0, \ \ \ \ \ 0}

        			\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ , 
        p2\  -> \ m2\ γ2 {1, 0, 0, \(-β2\)}

        			\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ , 
        p3\  -> \ m3\ γ3 {1, 0, 0, \ \ β3}}\)

conRule =  {p3  ->  p1 - p2}

eq1  =  
      (m3^2  ==  p3 . η . p3 /. conRule /. momRule /. 
            β2γ[β2, γ2]) // Simplify

sol  =  Solve[eq1, γ2] // Flatten

ken3  =  m2 γ2  -  m2  /. sol // Simplify