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Homework Help: How do you know what goes together to form a 4-vector?

  1. Nov 2, 2009 #1
    I've been studying relativity and standard model physics, and I don't understand how it is determined what 'things' go together to form a 4-vector. For example, there is the familiar energy momentum 4-vector, the charge-current density four vector, the phi-A (scalar/vector potential) 4-vector from electromagnetism, the frequency-wavevector four vector from special relativity, and so on and so forth.

    Apart from the fact that these quantities evidently DO transform as four-vectors, is there some first principle argument that shows what quantities will go together to transform as a four-vector, like say in quantum mechanics where non-commuting operators indicate the existence of an uncertainty relation between quantities? Like how would you know that charge density and current density would form components of a 4vector and transform like one?
  2. jcsd
  3. Nov 2, 2009 #2


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    Hi Astrofiend! :smile:

    If it turns up in a covariant equation, it has to be a spinor or a 4-vector or …

    If it's one-dimensional, it'll be a 4-vector. :wink:

    (eg current has dimension one, so it'll be part of a 4-vector, and so will its density)
  4. Nov 3, 2009 #3
    Cheers mate - appreciate the response! I'll have to go away and think it over a bit...
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