…definition. So we then have the rule, therefore, that xy is equal to delta of x minus y. It had to be invented by Dirac, because he's the guy who worked out this method of describing quantum mechanics. I would say immediately a point, which I think is…

…the forms of the equations that we use, the system of representations in different base states and so on, is due to Dirac. I would like to describe how this equation does do what Schrodinger wanted, which is to produce energy levels without... What time…

…to be in position x is orthogonal. And you would like to write that dyx. But in continuous variables, that isn't it. And Dirac had to invent the symbol to represent that. He wrote dy minus x. And I understand. that you've heard about the delta function…

…the problem is that everything we measure we make inferences about it. It's quite a complicated thing. You're not worried about what Dirac says you say because it's an inference like any other inference. Is that the point you're trying to make? Well, it…

…disturbing the system. That's vital to the ideas of quantum mechanics, or you're getting in trouble. And that's the thing that Dirac is trying to emphasize. One of the difficulties with quantum mechanics is that it was originally invented in a time in…

…equations which appear here. Incidentally, I cannot resist at this moment to tell you a rule which is called the formula due to Dirac. That makes you feel like you're really advanced. And what Dirac says is, look, he said, if you want to, you can write…

…moment to tell you a rule which is called the formula due to Dirac. That makes you feel like you're really advanced. And what Dirac says is, look, he said, if you want to, you can write this one as twice minus minus minus minus minus, can't you? Of…

…what you had begin with. If you flip the spins about when it's broad minus, right, you see? So the famous formula of Dirac is, that sigma of one particle. I'll call them electrons and protons. He calls them one and two. Sigma electron dot sigma proton…

…the equations those things which are common, which, you see, if I were to say this equation is true for any chi and any phi, Dirac has a nice idea. Instead of having to say an equation is true for any chi and any phi, just erase those things for…

…don't know what you're doing. But it's lots of fun. It all turns out to be all true equations. Incidentally, using the same notation as Dirac, we can get rid of this i, and you can make it more this way. And you can write that. And people do that.…

…solving the equation. But at the same time, there was a development or an understanding of the, particularly by Born and Dirac, of the physical ideas behind the quantum mechanics. As quantum mechanics developed further, it turned out that there were a large…

…the electron and some relativistic phenomena, that, however, behaved the same principles of quantum mechanics that were derived by Born and Dirac. So it has historically been so that all courses in quantum mechanics begin the same way. You first have to…

…no. Unfortunately, like the only reference that has the attitude that we're going to have in this lecture is a book by Dirac. But it's so... abstracted. It's so beautifully abstracted that it's almost impossible for you to read out of. It says all these…

…which I'll mention in a moment when I come to the end of the discussion of the different possibilities. Another possibility suggested by Dirac is this peculiar one. It's a sort of hocus pocus. He says, I say I admit that an electron does not act on…

…of Born and Infeld, have never been satisfactorily made into a quantum theory. The theory with advanced and retarded waves of Dirac or Wheeler and Feynman has never been made into a satisfactory quantum theory. This theory of BOP has never been made…

…mass. Well, yeah, but it depends on what level... Well, the whole thing depends on how you describe the field. If you take the Dirac equation, so you start with the A and the phi and have this magnetic moment come out secondhand, then if you go back…

…the equations One must understand the equations, and that means, not in a mathematical sense, but understand in a definition given by Dirac. He said, I understand what an equation means if I have a way of figuring out the characteristics of the solution…

…must necessarily be questioned. And that is the question, the relation between matter and antimatter. It became apparent at first Dirac predicted that although we have electrons, that there must be another particle, which is called a positron, discovered here…

…when you learn the quantum mechanics, the Schrodinger equation. For example, if the particle corresponds to non-relativistic energies, the Dirac equation, if it's an electron at relativistic or other energies, The Maxwell equations, if it's a photon that you're…

…nobody has really been able to understand in any direct fashion. An example, for example, is the common consequences of the Dirac equation, which come in a very beautiful mathematical way, but it's hard to understand. And in this particular sense, it looks…

…everything else in space. If you got rid of all the idlers and everything else in space, the thing was okay. Dirac discovered the correct laws of quantum mechanics for relativity, quantum mechanics, simply by guessing the equation. And the method of…