Homework Set # 5 - Due September 30
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1) 4.1.8
2) 4.1.9
3) 4.1.10
4) 4.1.11
5) The exponential in a plane wave is exp[i(k.r-ωt)].
We recognize xμ=(ct,x1,x2,x3)
as a prototype vector in Minkowski space. If ωt-k.r
is
a scalar under a Lorentz transformation, show that kμ=(ω/c,k1,k2,k3)
is a vector in Minkowski space. Hint: in Minkowski space the metric
tensor gμν=diag(1,-1,-1,-1).
Note: Multiplication by ħ
yields
(E/c,p)
as a vector in Minkowski space.