James Fodor

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3,084 appearances 4 recordings 1 series first heard Jun 2026 last heard 30 Aug

James Fodor’s voice in public audio — every appearance, attributed to the second.

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The Science of Everything Podcast · Episode 164: Gauge Theory and the Higgs Boson · 30 Aug 2026 podcast

And this gives rise to the extra degrees of freedom in the gl in the Lagrangian, which gives rise to the three bosons that uh then couple with and interact with the uh the corresponding fermion field.

So we have three of them instead of just the one because of the weak doublet structure.

And just as the invariance of the electron phase gives rise to conservation of electric charge, so too does this invariance with respect to rotations in in the sort of weak space, uh weak doublet space, gives rise to the conservation of weak flavor.

So that means that

uh so whenever for example we s we have an electron electron neutrino, uh those can interact in certain ways, but we always need to preserve the total amount of weak flav that version of weak flavor that we have before and afterwards.

So there's that's the corresponding conservation and also the um quantum properties that relate to the uh the force.

It's this weak flavor.

The group that describes the symmetries and transformations that we've just been talking about is called SU two, the the two being in brackets.

And this is the group that describes the the set of uh matrices that all transform between each other, um, which have a dimension of two by two and a determinant of one.

Now the the S stands for special, and there's a mathematical distinction between SU1 S U2 and then just U2, which is important, but I'm just I'm just not going to talk about that here, just to simplify things a little bit.

So basically, just in the U1 case, basically that just means it's it's a a group of one by one matrices, essentially, that uh describes transforms of of a very simple type.

In this case, we have a group of two by two matrices.

matrices which describe this rotation in uh weak phase space and this invariance of all of these um of transformations within that space because again it it doesn't matter what the phase is for each of our two fields in the weak doublet like the electron electron neutrino it's only phase differences that matter but now we've got two fields and so there's more interactions so

We we describe that with a two by two matrix instead of just like essentially a a scalar or a one by one matrix, if you like.

Because there are three generators of this group, three in other words, you can describe all of the matrices in this group as a combination of the th of three of of these three basic ones, uh the the generators.

Uh so that that's why we have three gauge bosons.

It's because essentially the space of redundancies of the number of internal degrees of freedom is described by three two by two matrices.

And so there's gonna be one for each of our gauge bosons.

So there's this nice symmetry between the mathematics and the physics.

There's three generators that describe invariances of our group of the two by two matrices that describe the invariances of the internal degrees of freedom of the extra phase terms that we have for our weak doublets.

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