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    Hi, can someone pleeeeease help me out with questions 5c and 5e please? I've got no idea how to go about them. for e I just can't work out what the covariant gauge transformation would actually be... I think from then on I'd be ok.

    Thanks
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    Sorry I only got a C at gcse physics o.0 ...
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    (Original post by TheRandomer)
    Hi, can someone pleeeeease help me out with questions 5c and 5e please? I've got no idea how to go about them. for e I just can't work out what the covariant gauge transformation would actually be... I think from then on I'd be ok.

    Thanks
    Do you know what the gauge transformations for \phi and \bold{A} are? You can generalise this to A^{\mu} using the four-gradient operator.
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    (Original post by suneilr)
    Do you know what the gauge transformations for \phi and \bold{A} are? You can generalise this to A^{\mu} using the four-gradient operator.
    Yeah I have A^{\mu} but I can't figure out how to get the covariant version.. because I know the sign of the grad bit will change, so if I try just subbing all the A^{\mu} for A{\mu} it doesn't work =/
    I'm just very confused. haha. I basically have the equation for the contravariant gauge transform but I need the covariant one..
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    (Original post by TheRandomer)
    Yeah I have A^{\mu} but I can't figure out how to get the covariant version.. because I know the sign of the grad bit will change, so if I try just subbing all the A^{\mu} for A{\mu} it doesn't work =/
    I'm just very confused. haha. I basically have the equation for the contravariant gauge transform but I need the covariant one..

    You use the metric  \mathbf{g} to change between covariant and contravariant forms, i.e.

     A_{\mu} = g_{\mu \nu}A^{\nu}

    See here for more info
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    (Original post by TheRandomer)
    Yeah I have A^{\mu} but I can't figure out how to get the covariant version.. because I know the sign of the grad bit will change, so if I try just subbing all the A^{\mu} for A{\mu} it doesn't work =/
    I'm just very confused. haha. I basically have the equation for the contravariant gauge transform but I need the covariant one..
    It should stay the same I think. The time components stay the same going between co/contravariant, whilst the spatial components will change sign which should cancel with the sign change of grad

    EDIT: Actually I've just read through the question again, and I don't think it wants the gauge transformation of  A_{\mu}. When it says "in covariant form", I'm pretty sure this means that it wants the transformation to be Lorentz covariant ie a tensor equation, rather than wanting the transformation written in terms of covariant objects. See here for more details on the usage of covariant.
 
 
 
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