Talk:Dirac equation

I think the whole idea of introducing the nonrelativistically covariant notation first before manifestly covariant notations in many topics, including the Dirac equation, is merely a reflection of historical inertia, of students being taught noncovariantly in turn teaching noncovariantly later... Phys 21:53, 15 Nov 2003 (UTC)

That's a little presumptuous. The advantage of the non-covariant notation is that it has the form of a Schrodinger equation, which emphasizes that the Dirac equation is a quantum mechanical wave equation. -- CYD

If you assume the Dirac equation is the first-quantized equation for a particle (But then, you'd have to explain the Dirac sea). But you know the correct interpretation for it is as a second-quantization of a classical relativistic field equation! Phys 18:22, 16 Nov 2003 (UTC)

To be precise, the Dirac field theory is obtained by the first quantization of a classical field equation; or, alternatively, the second quantization of the Dirac wave equation. I don't think either approach has any great advantage over the other. -- CYD

Unfortunately electrons are fermions, so introducing it initially as the quantization of a classical relativistic field equation means that you have to start out by introducing the students to the concept of a classical anticommuting field of Grassman variables, which could be pretty intimidating unless they are mathematicians... --Matt McIrvin 03:42, 17 Oct 2004 (UTC)

B = <math>\nabla<math> ×A Is that correct? I think there was a mistake and I tryed to correct it, but I do not know if it is correct.

Plàcid 21:33, 27 Jan 2004 (UTC)

Moved from article

I moved the following text from the article.

All upper explanations are old and wrong.The relativistic electron has only one positive energy and two different motions: one in forward and other in backward as which ot them contain spinning in right and in left. Terefore fore components of total function describe fore motions with equal energy.Three matrixes describe three strongly correlated oscillations in three mutually perpendicular directions. In result of this fermion strongly correlated motion (Zitterbewegung) there is no any difergence in electrostatic interactions known in classical approximation and there is only magnetic interaction between magnetic intensities of own magneric field and magnetic dipole moment of the relativistic quantized electron. In result of thie interactions is obtained self-energy of the relativistic quantized electron.

Comments, anyone?

Anville 23:39, 2 Nov 2004 (UTC)

Noninteracting sea?

By necessity, hole theory assumes that the negative-energy electrons in the Dirac sea interact neither with each other nor with the positive-energy electrons. Without this assumption, the Dirac sea would produce a huge (in fact infinite) amount of negative electric charge, which must somehow be balanced by a sea of positive charge if the vacuum is to remain electrically neutral. However, it is quite unsatisfactory to postulate that positive-energy electrons should be affected by the electromagnetic field while negative-energy electrons are not.

While it's true there appears to be a problem with an infinite negative chage density, the early pioneers of QED assumed the charges of the proton sea would cancel out the charges of the electron sea. It was never assumed the negative energy electrons are not affected by the electromagnetic field. Otherwise, a hole (positron) would not be deflected in the opposite direction by an electromagnetic field. The positive energy electrons also interact with the negative energy electrons. This is necessary for computing the vacuum polarization. Phys 02:57, 14 Jan 2005 (UTC)

Yes, I don't know what I was thinking when I wrote that. Thanks. -- CYD

General Relativity

I miss something about the Dirac-Equation in curved space. Can someone add it? --141.63.56.202 08:29, 14 Apr 2005 (UTC)