Bernard Kelly deleted ___gamma2.tex  about 10 years ago

Commit id: c0741028c4dc5b858b29cc2835920b31fd695048

deletions | additions      

         

& = & \gamma^2 v^m v^n \ell_{m,n}\\  & = & - \left[ \delta^m_i + ( \gamma - 1 ) \frac{v^m v_i}{v^2} \right] \gamma v^n \ell_{m,n}\\  & = & - \gamma v^n \ell_{i,n} - \gamma ( \gamma - 1 ) \frac{v^m v^n v_i}{v^2} \ell_{m,n}\\  & = & - \left[ \delta^n_j + ( \gamma - 1 ) \frac{v^n v_j}{v^2} \right] \gamma v^m \ell_{m,n}\\  & = & - \gamma v^m \ell_{m,j} - \gamma ( \gamma - 1 ) \frac{v^m v^n v_j}{v^2} \ell_{m,n}\\  \ell_{i',j'} & = & \Lambda^{m}_{\,\, i'} \Lambda^{n}_{\,\, j'} \ell_{m,n}\\  & = & \left[ \delta^m_i + ( \gamma - 1 ) \frac{v^m v_i}{v^2} \right] \left[ \delta^n_j + ( \gamma - 1 ) \frac{v^n v_j}{v^2} \right] \ell_{m,n}\\  & = & \left[ \delta^m_i + ( \gamma - 1 ) \frac{v^m v_i}{v^2} \right] \left[ \ell_{m,j} + ( \gamma - 1 ) \frac{v^n v_j}{v^2} \ell_{m,n} \right]\\  & = & \ell_{i,j} + ( \gamma - 1 ) \frac{v^n v_j}{v^2} \ell_{i,n} + ( \gamma - 1 ) \frac{v^m v_i}{v^2} \ell_{m,j} + ( \gamma - 1 )^2 \frac{v^m v_i}{v^2} \frac{v^n v_j}{v^2} \ell_{m,n} \\         

___gamma.tex  The_derivatives_of_t.tex  H_alpha.tex  ___gamma2.tex  brace_ds2__.tex  brace_gamma_i_j_.tex  subsectionzBoosted_I.tex