Schwinger’s Measurement Algebra Lives!

Back in the 1950s, Julian Schwinger invented a version of QM / QFT that is now known as Schwinger’s measurement algebra. I’ve been working on this for years, pretty much alone. Now I have company, with an article just published by Wlodzimierz M. Tulczyjew on arXiv: Density Operators and Selective Measurements, math-ph/0711.2258.

As it turns out, none of what Tulczyjew has published is new. I’ve been promoting the tight relationship between density matrix formalism and Schwinger’ measurement algebra for years. However, I’ve been promoting it outside of academia. The news is this idea (a) having more than just me working on it, and (b) ending up on arXiv. Maybe he will publish it later.

Another paper that is similar to what I’m working on (and have linked in on this blog a lot) is Quantum Electrodynamics of Qubits, quant-ph/0705.2121 by Iwo Bialynicki-Birula and Tomasz Sowinski. This paper has passed peer review and been published as Physical Review A 76, 06106 (2007).

My paper on the application of Schwinger’s measurement algebra to the problem of classifying quantum bound states is coming along. I’ve been keeping the latest version up on the web here. It’s intended for Foundations of Physics. It derives a general mass formula that relates three masses for particles with identical quantum numbers (other than mass) that are color bound states. There are two formulas needed:
Mass formulas
where the real constants v and s depend on the resonance series. The “v” is for “valence” while “s” is for “sea”. The idea is that the “v” part of the formula describes the things that are shared by the three states, while the “s” gives the difference. That is, any given set of resonances should have the same valence quarks; where they differ is in the sea.

The same formulas applies (and were originally discovered) to the charged leptons and the neutral leptons (neutrinos). In the case of the charged leptons, v and s are related by the square root of 2 and the formula gives Koide’s mass formula for the charged leptons which famously predicted the mass of the tau back in 1981.

I’m most of the way through writing the section on the neutrino mass formula. After that comes a bear of a section, the applications to the mesons. There are hundreds of mesons and, consequently, several dozen mass formulas. Some of the mesons are rather involved and there is choice in how one organizes them. This is both good and bad.

5 Comments

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5 responses to “Schwinger’s Measurement Algebra Lives!

  1. Pingback: EquMath: Math Lessons » Blog Archive » Schwinger’s Measurement Algebra Lives!

  2. Pingback: History of Mathematics Blog » Blog Archive » Schwinger’s Measurement Algebra Lives!

  3. Kea

    Carl, I think one can expect a number of arxiv papers closely related to your work in the near future. After all, anyone can read your stuff.

  4. carlbrannen

    Actually, the above two formulas work for the charged lepton type objects. The corresponding formula for the neutrino type objects has an extra term, \pi/12 or \pi/4 in the angle of the trig function.

    And I’m writing the section on the mesons right now.

  5. Hi, bro!

    Good to hear from you — no, no mines under Nutwood. Under Bear’s Retreat, yes, but we’ve got mine insurance — that’s the best one can do. But Nutwood’s not undermined.

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