Massive Vector Boson

  1. ChrisVer

    ChrisVer 2,403
    Gold Member

    Starting from the Lagrangian density:
    [itex] L= -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{m^{2}}{2} B_{\mu}B^{\mu}[/itex]
    we can derive the E.o.M. for the field [itex]B[/itex] which read:

    [itex] ( \partial^{2} + m^{2}) B^{\mu} - \partial^{\mu} (\partial B) = 0 [/itex]
    In the case of a massive field, I am not sure how I can kill out the partial of B through the field equations....
    [itex] \partial B=0 [/itex]
    Does this come as a constraint/boundary condition of minimizing the action? or is there something I cannot see? In most cases they state it's a Lorentz Gauge, however I am not sure how this can be indeed shown...
    Last edited: Apr 21, 2014
  2. jcsd
  3. ChrisVer

    ChrisVer 2,403
    Gold Member
    P.180 , eq 19,20 and the 1st paragraph of p.181 gave the answer... One has to take the derivative of the Equations of Motion [itex]\partial_{\mu}[/itex] and [itex]\partial B[/itex] comes out zero... (unfortunately for me I came out with the wrong EoM missing a minus sign and I couldn't even think of doing it)
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