こんにちは、
epdash = (1/Sqrt[2])*{0, Cos[theta], 1, Sin[theta]};
としますと、kdashとepdashの内積が、"0"になりません。

下記のどこが間違っているでしょうか？



k0 = pi3;
k1 = 0;
k2 = 0;
k3 = -pi3;

kdash0 = pi3;
kdash1 = -pi3*Sqrt[1 - z^2];
kdash2 = 0;
kdash3 = -pi3*z;

episilon0 = 0;
episilon1 = (1/Sqrt[2])*1;
episilon2 = (1/Sqrt[2])*1;
episilon3 = 0;

(*この部分は正しいでしょうか？*)
episilondash0 = -1;
episilondash1 = Sqrt[1 - z^2];
episilondash2 = 1;
episilondash3 = z;
(*-------------------------*)

Simplify[episilondash0*episilondash0 - episilondash1*episilondash1 - episilondash2*episilondash2 - episilondash3*episilondash3]
Simplify[episilon0*episilon0 - episilon1*episilon1 - episilon2*episilon2 - episilon3*episilon3]
Simplify[kdash0*kdash0 - kdash1*kdash1 - kdash2*kdash2 - kdash3*kdash3]
Simplify[episilondash0*kdash0 - episilondash1*kdash1 - episilondash2*kdash2 - episilondash3*kdash3]
Simplify[episilon1*episilondash1 + episilon2*episilondash2 + episilon3*episilondash3]