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Natural Science Forum / Physics / Particle Physics / June 2007Why is the Weinberg angle an angle?
Can somebody explain in simple words why the electroweak unification is described by an ANGLE? What is the geometrical representation where this angle appears? (Or are there several of them?) Thank you in advance! Francois First, it's not the Weinberg angle. It's the "weak mixing angle" and was first defined by Glashow in 1961. Second, it's defined as an acute angle of a right triangle whose sides are the SU(2)_weak,L gauge coupling "g" and the U(1)_hypercharge gauge coupling "g'". | | g' theta_W | --------------------- g The weak mixing angle theta_W is defined by: tan(theta_W) = g' / g. So it is angle. Standard modern treatments of gauge theories and particle physics discuss these points. See also the Review of Particle Physics 2006. > Can somebody explain in simple words > why the electroweak unification is described by an [quoted text clipped - 4 lines] > > Francois > First, it's not the Weinberg angle. It's the "weak mixing angle" and was > first defined by Glashow in 1961. [quoted text clipped - 14 lines] > Standard modern treatments of gauge theories and particle physics discuss > these points. See also the Review of Particle Physics 2006. Hmm. One could define an angle for any two positive quantities g`and g in this way. So it does not need to be an angle at all, in the end? Or is there another reason that the ratio g'/g is interpreted as the tan of an angle? (For example, why are g' and g drawn on orthogonal axes? Is there a reason for this?) I am just trying to understand - I hope this does not sound obnoxious. Francois On Jun 6, 12:19 am, francoisbelf...@yahoo.fr wrote: > > First, it's not the Weinberg angle. It's the "weak mixing angle" and was > > first defined by Glashow in 1961. [quoted text clipped - 26 lines] > > Francois It's not. The mixing matrix is a unitary matrix, and a unitary matrix can always be represented using an angle, whether that angle is a real angle or not. It's just shorthand. Lorentz boosts look like angular rotations, too, almost. Enough to call give the angle a name: rapidity. PD > It's not. The mixing matrix is a unitary matrix, and a unitary matrix > can always be represented using an angle, whether that angle is a real > angle or not. It's just shorthand. > > Lorentz boosts look like angular rotations, too, almost. Enough to > call give the angle a name: rapidity. Angula (Croocks) are foolish. Use a damned fraction, say, in floating decimal: .07983 or .31932*.25. > > It's not. The mixing matrix is a unitary matrix, and a unitary matrix > > can always be represented using an angle, whether that angle is a real [quoted text clipped - 5 lines] > Angula (Croocks) are foolish. Use a damned fraction, say, in floating > decimal: .07983 or .31932*.25. Oh yeah, ratios are best: .54836. |
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