dirac

They are cousins of the Dirac equation (think about how a Dirac point and a Weyl point are related).

Sometimes our intuition is simply wrong, so unintuitive edge cases like Dirac spikes end up being fundamental tools in physics and signal analysis.

From your description, Dirac seems to be one of those wise geniuses.

In your example of a single charge moving at velocity v, which passes through the origin of your coordinate system at time t, the current density at the origin is basically a Dirac delta function.

You can also think of a Dirac delta function as a finite but normalised Gaussian (or normal) distribution of charge, which gets rid of the discontinuities.

The BBC's a good example, how long have they been working on their own Dirac codec?

Seconded on convolution and the Dirac delta.

You seem to be implying that the BBC's Dirac work has produced no useful results; I would disagree.

I misspoke here, I meant Dirac or Majorana fermions.

So, the set of all distributions form a monoid under convolution if you allow the Dirac delta-function to act as `mempty` -- in a certain representation, this appears as the termwise-summing monoid.

In other words, there is zero current density through that point at all times other than at one instant (vt) where it would be infinite (although finite when integrated over time, basically how Dirac delta functions work).

So, just as a quick overview, there are two ways within the Standard Model to give a particle mass, one is the Higgs mechanism where the particle couples with a field generating an effective Dirac mass; another is to sum up certain Feynman diagrams (loops and other particles and such) generating a Majorana mass.

This is where Einstein came in, who published his general theory of relativity at 26, and Dirac, who wrote the “fever chill” poem.

That aside, there is a mathematically well-defined sense in which Weyl fermions are the most "fundamental" fermions: the other kinds you hear about, Dirac and Majorana, can all be written as combinations of Weyl fermions.

In the 1940s Dirac commented bitterly, in view of problems quantum field theory was having at the time: “Then, a second-rate physicist could do first-rate work – now, it takes a first-rate physicist to do second-rate work”.

As far as the "Popularity" - I'm sure there are groups of theoretical physicists that work purely on the assumption of one or the other, but most treatments I've seen cover both the cases for Dirac and Majorana neutrinos, given that we don't have evidence one way or the other.

To make a Dirac, you take two Weyls of opposite helicity and couple them with a common mass term.

Could a startup get VC funding if it wanted to develop something like Dirac, which doesn't do anything groundbreaking?

Dirac is the one whom people find most surprising, because he set up the whole foundation, the general framework of quantum mechanics.