Feynman's 1986 Dirac Memorial Lecture

He talked about antiparticles, CPT, spin, and statistics



You may watch those 70 minutes. Feynman starts by saying that Dirac has been his hero so he was honored to give a Dirac lecture. Dirac was a magician because he could guess the right equation, a new strategy to do science.

However, Feynman also says that Dirac also invented Zitterbewegung which wasn't terribly useful. Well, not only that: Zitterbewegung is completely unphysical. However, it wasn't invented by Dirac but by Schrödinger as the German name of the non-effect indicates. ;-) Dirac wouldn't make such an elementary mistake when it came to basic quantum mechanics.




However, Feynman quickly returns to the marriage of special relativity and quantum mechanics: antiparticles are essential for the union. He was going to focus on antiparticles and the Pauli exclusion principle.

Without particle-antiparticle production, the antisymmetry of the wave function would boil down to the initial state – God knows why it's the way it is – and the antisymmetry would just be preserved by the evolution. However, it gets more interesting because new particles may be produced and the wave function is still antisymmetric in them.

Feynman began to talk about amplitudes for processes with particles and antiparticles. Unfortunately, the transparencies are not too readable. Can you find a better quality video somewhere? Well, the camerawoman didn't look at the slides most of the time, anyway.

At any rate, he says that the Fourier transform composed of positive-frequency modes only is inevitably non-vanishing in each interval. You need negative frequencies as well if you want things to vanish in the past or outside light cones which is needed for causality. The negative-energy objects have to be a part of physics in some way.

Virtual particles have to exist and one man's virtual particle is another man's virtual antiparticle, not to mention women's antiparticles :-), simply because the sign of energy of spacelike energy-momentum vectors depends on the reference frame. So the antiparticles' properties are actually fully determined by particles' properties because of relativity.

Feynman mentioned that he had never pronounced "probability" correctly because he didn't have the patience. LOL.

He explains why the fermions cancel diagrams to impose the Pauli exclusion principle, something that doesn't hold for bosons such as spin \(j=0\) particles (Feynman confusingly talks about photons with \(j=1\) just seconds earlier).

The Bose-Einstein statistics isn't hard to understand whenever we talk about oscillations. The Fermi-Dirac statistics may be more counterintuitive so of course some special attention is invested into explanations of the minus signs for fermions.

A segment of the lecture in which the (invisible) math formulae are important is dedicated to clarifying the Feynman propagator – why it's the right way to combine the retarded and advanced propagators' features. Unfortunately, he's too modest to call it "Feynman propagator" so you may have a problem to determine what he's really talking about here. ;-)

The CPT-theorem is explained in the same way I am doing it (independently). The CPT-operation is really just a rotation of spacetime. In the Minkowski space, there's also the mysterious nowhere land, the spacelike region, but with continuations to the Euclidean space, the CPT-operation simply is just a rotation by 180 degrees. So the world has to be invariant under it. (The C, charge conjugation, is an internal operation that is automatically included in the operation because if a particle goes backwards in time, as seen on the arrow of the 4-vector \(j^\mu\), and it does go backwards if we perform the T, the time reversal, then e.g. the charge \(\int\dd^3 x\,j^0\) reverts the sign.)

Around 29:00, the fermions change the sign of the wave function with rotations under 360 degrees: \(\exp(im\phi)\) just gives you that. Intuition wouldn't be enough. At 30:00, he reviews the Dirac's belt trick, a physical exercise showing that a rotation by 720 degrees is like doing nothing while a 360-degree rotation twists your arm. A huge applause follows.

The rest of the lecture is about a careful tracing whether you did the rotation or not. Without clearly readable transparencies, the technical stuff may be a bit hard to follow. He calculates \(T^2\) which has to change the state at most by a phase but the phase may be nontrivial. There are differences for bosons and fermions...

At 57:50, Feynman discusses a permuted connection between two loops – attributed to a Mr Finkelstein – that could be instantly used as an explanation of your humble correspondent's matrix string theory. ;-)