
#19
Dec912, 05:05 AM

P: 136

The coupling constants are parameters of the theory. Whatever their values, there will exist a value of θ that yields a massless photon.
They are also related to the electromagnetic coupling constant [itex]e[/itex] by the relation [itex]e = g_L\ sin (\theta) = g_Y\ cos (\theta)[/itex] So by measuing [itex]e[/itex] and [itex]\theta[/itex] we can immediately determine their values. 



#20
Dec912, 08:29 AM

PF Gold
P: 305

this reminds me a previous thread where I defended the idea that the electric charge (as g and g') was defined before symbreaking. (and that theta value was given before it)




#21
Dec912, 09:21 AM

P: 136

But surely the thing that isn't defined until symmetric breaking is the "direction" within the SU(2) "space" along which it breaks. Isn't this analogous to the difference between empty space where there is no magnetic field, when there is no preferred direction, and when a magnetic field is present in which case it introduces a "preferred" direction namely that of the field?
In choosing three basis generators T_{1}/T_{2}/T_{3} for an SU(2) space, we are implicitly defining a set of arbirary "axes" within it. Without symmetry breaking, we could if we wanted then rotate those into a different set, say T'_{1}/T'_{2}/T'_{3}, with no change to the resulting physics. When the symmetry breaks we find there is a "direction" within the SU(2) space in which the weak isospin assignments of particles  which ab initio is an orientation defined by a pair of complex numbers, cf electron spin  now contributes to something we observe as the particles' electric charges. 


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