Relativistic Quantum Mechanics

  • #1
I've been writing a paper on Relativistic Quantum Mechanics. I'm still writing, but I think some of the results I have so far are interesting enough to show around. I've shown this to some Physics Professors I know plus a Physics grad in Tehran has agreed to take a look, but I thought I should cast a wider net. I'm not looking for anyone to tell me the results are correct or physically valid, but only that it is a serious attempt. I would like to find a sponsor so that I can publish in the quantum mechanics section of In my paper I have proposed a Lorentz invariant Schrödinger equation for a scalar wave function, which separates into the ordinary time independent Schrödinger equation. With the Lorentz invariant equation I obtained a probability density 4-current, and I am currently working on the section on relativistic angular momentum operators which is where I've left off while I hit the books in order to proceed further. Here's a link to my paper which is currently 110 pages. Quantum Mechanics 5.18.09.pdf [Broken]
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Answers and Replies

  • #2
Well, I have to ask what the purpose of this text is, since there are many textbooks on relativistic quantum mechanics out there.

Do you cover essential concepts in relativity such as causality?
  • #3
I agree with glenn here. You want to know if it's a serious attempt. A serious attempt at what?

You should really explain, at least in your work if not here, what you intend/purport to do.
  • #4
I also mean, after reading a bit of your text, you don't consider what all other text does - is the wavefunction 0 outside the lightcone? (i.e causality is preserved). causality is not even mentioned ONCE is the entire text! If your intention is to construct a causal and physical relativistic quantum mechanics, you have failed badly I would say. Lorentz invariance is just one side of the story.

If you never have read about relativistic quantum mechanics in textbooks, it's weaknesses are covered in the intro chapters of e.g. Weinberg - Quantum Theory of Fields, Srednicki - Quantum Field Theory, Peskin - intro to Quantum field theory.

Best Regards,
  • #5
My purpose is to learn the subject, and you answered one question I had as to whether you could recommend a good textbook on the subject.
  • #6
My purpose is to learn the subject, and you answered one question I had as to whether you could recommend a good textbook on the subject.

Well, learning by writing a paper which does not include the standard reference books on that particular subject is not hit.

These texts are considered to be the standard references:

Relativistic Quantum Mechanics by Bjorken and Drell

Advanced Quantum Mechanics by Sakurai

Newer references:

Relativistic Quantum Mechanics and Field Theory by Gross

Relativistic Quantum Mechanics. Wave Equations by Greiner

You can also check out the three references I gave you earlier, all which deals with relativistic QM's weaknesses.

It is possible to construct a Schrödinger equation for which the wavefunction decays exponentially outside the lightcone - which is not good - but enough for some applications. Rather use Klein-Gordon and Dirac Equation - which preserves causality but does not "obey" the premisses of QM.

Your text was very nicely written and organized, very nice. But you have to motivate WHY you are writing it and also consult texts on Relativistic Quantum Mechanics.

So it is a serious attempt, but you have neglected two major issues:
i) Is causality preserved? (I can tell you in your case that it is not)
ii) What has already been explored/researched/written in this area?

You are telling us that you have done a serious attempt to do Relativistic Quantum Mechanics, in order to learn?
  • #7
My purpose is to learn the subject, and you answered one question I had as to whether you could recommend a good textbook on the subject.
One good reference could be the excellent lecture notes on introductory quantum field theory by David Tong. In" [Broken] there is nice discussion about causality and how to recover the non-relativistic theory. I think you should take a quick look.

But I really liked your text, keep up the good work!
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  • #8
Thanks for the responses I'll try to locate the text by David Tong. I'm brazen and foolish enough try to figure things out for myself, but neither do I want to reinvent the wheel. My other purpose was to see if the Lorentz invariant Schrödinger equation for a complex scalar wave function that I've chosen to examine exists elswhere in the literature. The equation I'm examining separates for a time independent potential (stationary with respect to the obsevrver) into the familiar time independent equation, but the operator i\hbar\partial\partial t no longer represents the total energy. It is now on equal footing with the momentum operators and represents the rest + kinetic energy. I am only aware of the Dirac equation as a relativistic quantum mechanical equation, with a 4-vector wave function. What I'm considering is a scalar wave function. Since it is a work in progress, my hobby, I haven't examined causality. I'm currently boning up on tensor caculus and spin. Causality will have to wait. But thanks for having a look. Oh I fixed some typos and notation

"[PLAIN [Broken] Quantum Mechanics 5.21.09.pdf"] [Broken] Quantum Mechanics 5.21.09.pdf[/URL]
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