Lorentz Transformation - Transformation of Other Physical Quantities

Transformation of Other Physical Quantities

For the notation used, see Ricci calculus.

The transformation matrix is universal for all four-vectors, not just 4-dimensional spacetime coordinates. If Z is any four-vector, then:

or in tensor index notation:

in which the primed indices denote indices of Z in the primed frame.

More generally, the transformation of any tensor quantity T is given by:

T^{\alpha' \beta' \cdots \zeta'}_{\theta' \iota' \cdots \kappa'} = \Lambda^{\alpha'}{}_{\mu} \Lambda^{\beta'}{}_{\nu} \cdots \Lambda^{\zeta'}{}_{\rho} \Lambda_{\theta'}{}^{\sigma} \Lambda_{\iota'}{}^{\upsilon} \cdots \Lambda_{\kappa'}{}^{\phi} T^{\mu \nu \cdots \rho}_{\sigma \upsilon \cdots \phi}

where is the inverse matrix of

Read more about this topic:  Lorentz Transformation

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