where \(\gamma = rac{1}{\sqrt{1-v^2}}\).
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- Under a Lorentz boost along the x-axis with velocity \(v\), the metric tensor remains \( \eta^{\mu
- u} = ext{diag}(1, -1, -1, -1) \), and the transformation matrix \(\Lambda\) is:
- \[ \Lambda = egin{pmatrix} \gamma & -\gamma v & 0 & 0 \ -\gamma v & \gamma & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{pmatrix} \]
- The transformed tensor is \( T'^{\mu
- u} = \Lambda^\mu_{lpha} \Lambda^
- u_{eta} T^{lphaeta} \).
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