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Starting from the Lagrangian density:
L= -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{m^{2}}{2} B_{\mu}B^{\mu}
we can derive the E.o.M. for the field B which read:
( \partial^{2} + m^{2}) B^{\mu} - \partial^{\mu} (\partial B) = 0
In the case of a massive field, I am not sure how I can kill out the partial of B through the field equations...
\partial B=0
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...
L= -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{m^{2}}{2} B_{\mu}B^{\mu}
we can derive the E.o.M. for the field B which read:
( \partial^{2} + m^{2}) B^{\mu} - \partial^{\mu} (\partial B) = 0
In the case of a massive field, I am not sure how I can kill out the partial of B through the field equations...
\partial B=0
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...
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