James Fodor

speaker

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.

Trend

recordings per month · last 12 months

Recordings per month over the last 12 months — 4 in all, peaking in Aug 2026 with 2.

Appearances

newest first · ▶ plays the moment

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

All we had to do was re was read the form of the interactions off of our Maxwell's equations and then add this extra constraint to fix the gauge or to ensure that the gauge choice didn't matter specifically, by turning the global invariance into a local invariance and then applying.

applying the transformation and then we work out, oh now now the theory works.

Now, there's an extra key thing that we need to understand about this um gauge theory sort of solution to this problem, and that it requires that the fermion field, like the electron field in this case, is coupled in a certain way with a gauge field.

In this case, that's the photon field.

So there's a direct mathematical connection between requiring this local phase invariance to these transformations of the phase that can be different in every every place.

and coupling between the electron field and the electromagnetic field.

Coupling meaning there's an interaction between them.

They they interact with each other.

Like in the Feynman diagrams, you think about the lines coming in and lines coming out, right?

That's that's an interaction we're talking about, a coupling.

And that's exactly why we call the photon a gauge boson, because it's the particle that interacts with the fermion field uh to generate or to facilitate this local gauge invariance.

Or to put it another way, every gauge every local gauge invariance will necessitate the existence of a gauge field, which will then describe the uh field that that mediates interactions between fermions.

We can loosely uh think about this as if the virtual photons that are constantly being emitted and absorbed and are fluctuating in and out of existence by uh say different electrons as they're interacting with each other, uh th this sea of virtual photons uh that are being exchanged between them is carrying information about the phase of each ph of each electron.

And the exchange of of photons uh effectively ensures that there's this local uh invariance to to the phase, that um that information's constantly being moved about between points in the electron field um by photons to to maintain that local gauge invariance.

I mean, you shouldn't take that story too literally, but I think it's a helpful way of picturing the connection between this mathematical property of local phase invariance and the existence of this boson field that mediates interactions between the electrons.

You can think of the photon field as as consisting of these virtual particles that are exchanging phase information, constantly moving.

moving it about to ensure that there's this invariance between the different electrons.

Yet another way to describe this mathematically is that local phase invariance equals coupling with a gauge field.

So if we want to

get our particles to interact with each other uh through a an intermediate an intermediary force particle, we need to couple them to a gauge field, and we can do that by introducing or requiring mathematically this invariance of the the field to certain types of local phase transformations.

Showing 181–200 of 3,084 · page 10 of 155