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

1. Nov 2, 2009

### Astrofiend

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. Nov 2, 2009

### tiny-tim

Hi Astrofiend!

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.

(eg current has dimension one, so it'll be part of a 4-vector, and so will its density)

3. Nov 3, 2009

### Astrofiend

Cheers mate - appreciate the response! I'll have to go away and think it over a bit...