# time- and spacelike vectors

29 Jun 2016If you consider the action integral of Maxwell-electrodynamics,\(S = \int\mathrm{d}^4x\sqrt{-\mathrm{det}(\eta)}\:\frac{1}{4}\eta^{\alpha\mu}\eta^{\beta\nu}F_{\alpha\beta}F_{\mu\nu} + \frac{4\pi}{c}\eta^{\alpha\beta}A_\alpha\jmath_\beta\), one realises that \(\jmath_\beta\) is timelike with (covariant) components \(\gamma(c\rho,\beta c\rho)\) as it represents a moving charge distribution. What can you say about the vector potential \(A_\mu\)? Is it timelike, spacelike or null? Would it change under gauge-transformations?