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I am currently studying special relativity in depth for the first time, and have just encountered the concept of a Lorentz-invariant scalar field, $V(x,y,z,t)$. As I understand it, this is a scalar field for which the value, evaluated at any spacetime event, is independent of reference frame. My question is twofold.

  1. Is this the correct definition of a Lorentz invariant scalar field?
  2. How does such a field transform under a change of reference frame: i.e. if I transform my spacetime coordinates by the Lorentz transformation $\Lambda$, such that my new coordinates $(x',y',z',t')$ = $\Lambda(x,y,z,t)$, what is the new function $V'(x',y',x',t')$ in terms of $V(x,y,z,t)$?
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    $\begingroup$ You answered your own question: "the value, evaluated at any spacetime event, is independent of reference frame". $\endgroup$ Commented Aug 18 at 11:27
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    $\begingroup$ Scalar fields are really Lorentz covariant, not invariant. $\endgroup$ Commented Aug 18 at 14:07

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