So I've been playing around with different electroweak lagrangians (sourceless, higgsless, unbroken, broken, etc), and finding the equations of motion for them. Everything looks about right, but the issue I'm having is when you add in the masses of the weak bosons(no higgs though).This breaks the gauge symmetry of the U(1) and SU(2) fields, and should therefore also break the conservation law for weak hypercharge and isospin (of course there would still be a conservation law and gauge for the combination of hypercharge and isospin corresponding to the E&M field). And when I solve for the equations of motion, I do end up with the equations:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\partial^\mu{Y_\mu} = \partial^\mu(m_B^2B_\mu+M_a^2W_\mu^a)[/tex]

[tex]\partial^\mu(I_\mu^a+J_\mu^a) = \partial^\mu(m_a^2W_\mu^a+M_a^2B_\mu)[/tex]

where [tex]m_a[/tex] and [tex]M_a[/tex] are mass terms, and [tex]J_\mu^a[/tex] is the current of the a'th component of weak isospin due to the fields themselves.

These equations show that hypercharge and isospin are notnecessarilyconserved. However, from what I've read all 4 of these currents should be conserved. My question is whether this is just a postulate taken from experimental results or if I'm missing some theoretical reason that these currents must be conserved.

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# Conservation of weak hypercharge and isospin

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