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.

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

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

Now, that might sound a bit crazy, like, well, surely that will create differences between the uh phase at different points.

But actually it turns out that it doesn't.

And the reason is because there are other terms in the Lagrangian that cancel out the changes that are brought about by the transformation.

So when we make this transformation, this local transformation, that allows the phase to be shifted by different amounts at each point, there is now a this gets.

It's a bit technical, but I just want to illustrate why this happens.

There's a bunch of derivative terms in the Lagrangian, which uh mean that we have to take the derivative of the field, how the field changes in space-time, uh, and then that gives rise to certain terms like the kinetic terms, for example.

When we shift the phase by a constant amount, if you know anything about calculus, constants come out of the derivative.

When we differentiate a constant, it it doesn't change it, right?

Like the derivative constant is just zero.

So a constant global transformation is is unaffected by derivatives.

But local transformations are a function of x, and so they are affected by derivatives.

And this means we pick up an extra term when we take the derivative.

Which then adds an extra term in Alagrangian, which turns out to cancel out just the other terms that we had in there to mean that it's now gauge in the theory is now gauge invariant.

We we we still need to choose a gauge, but it doesn't matter which gauge we choose.

Whereas previously it the choice of gauge affected the result, uh, which was bad.

We don't want that to happen.

So this was great, right?

Um this introduction of this local gauge transformation.

Meant that we were able to solve this problem of the results depending on the gauge.

And now we have a quantum field theory of electromagnetism.

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