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As I understand, Dirac equation was first interpreted as a wave equation following the ideas of non relativistic quantum mechanics, but this lead to different problems.

The equation was then reinterpreted as a field equation and it is now a crucial part of quantum field theory.

My question is: could you provide me a reference (paper, book) that explains this evolution, including the different historical steps, etc. ?

I have a good knowledge of QM and I studying field theories, but I would like to have a clearer view on this historical evolution.

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up vote 5 down vote accepted

For the details of the physics involved in the two ways of interpreting the Dirac wave equation I recommend chapters XI and XII of Dirac's "Principles of Quantum Mechanics" 4th edition, and chapters XX and XXI of Messiah's "Quantum Mechanics", vol. II. For the more historical details I recommend chapters 5 and 6 of Crease and Mann's "The Second Creation", chapters 13 and 15 of Pais' "Inward Bound" and the first chapter of Schweber's "QED And The Men Who Made It".

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What a precise answer, I'll have a look at these ! – Cedric H. Nov 14 '10 at 11:57

I think that the first volume of the series "The Quantum Theory of Fields", by Steven Weinberg, is a good text to understand the origin of Dirac equation, QFT, and all these kind of topics.

Maybe Weinberg's books are not the best for a first course in QFT (or in General Relativity, he has also a great book on this topic), but his great coverage and unique point of view make them very worth reading.

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@Cedric: It's true that the notion of "fields" (as we have today in QFT) is something that wasn't completely developed at that time. But i never heard that Dirac's Eq was understood as a "wave equation": he was trying to explicitly describe particles (electrons) — besides, the notion that "particles" and "waves" were connected already existed at that time, in the form of von Neumann's "transformation theory" (read: Fourier Transform + distributions). On to of that, people knew that "Matrix Mechanics" (à la Heisenberg) and "Wave Mechanics" (à la Schrödinger) were two sides of the same coin (one being particle-like and the other one being wave-like).

So, before anything else, it'd be nice to corroborate this story of yours. ;-)

In any case, let me give you a couple of references that may shed some light:

  1. An Interpretive Introduction to Quantum Field Theory;
  2. From the Rise of the Group Concept to the Stormy Onset of Group Theory in the New Quantum Mechanics (PDF, 739Kb).

Hope this helps.

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I meant "wave equation" to mean "not a field equation". I'll have a look at your references, thanks. – Cedric H. Nov 14 '10 at 11:56

If you are interested in the origins, I think you must start the history with Sommerfeld. It is Sommerfeld who gets the fine structure levels, via an amazing cancellation of two mistakes (Bohr-Sommerfeld quantisation and lack of spin). So Dirac is sailing with a clear goal: his results must agree with Sommerfeld in some way. And of course Sommerfeld orbits are already the relativistic correction to Bohr orbits.

If you are more worried about the evolution towards field theory, I'd add Sakurai books to the Bjorken-Drell lot. Also Mandl.

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I recommend J.D. Bjorken, S.D. Drell, Relativistic Quantum Mechanics.

I think this book can provide smooth introduction into Dirac equation - the book is almost dedicated to it. At the same time I discourage starting with Quantum Field Theory before learning Dirac equation - the conceptual step may be way to difficult.

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In my opinion, a good introductory text for Relativistic Quantum Mechanics is Quantum Field theory- by Itzykson and Zubor. Another text is Relativistic quantum mechanics of string fields by - Greiner and Muller

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Although not directly relevant to your question, it is helpful to compare the different editions of Dirac's Principia. He revised his treatment of QED every time, and such an evolution must shed light on the evolution of the Dirac eq. from a one-particle eq. to its current status as a QFT equation. I cannot quite recommend any of Greiner's books, although i myself consult them all the time, I have the distinct impression ..... there is a kind of vagueness about his style which contrasts badly with the styles of the other texts that the posters here have recommended. I fear that that is a symptom of something.

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