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I think I found a physics error; is it, and what to do?

I think I have found an error in the entry for: gauge, n.

look at the fourth entry for meaning C. (physics) which I reproduce below (cut and paste from the OED website).

1940 W. Pauli in Physical Rev. 15 Oct. 718/1 By ‘gauge-transformation of the first kind’ we understand a transformation U→UeiαU→Ue—iα with an arbitrary space and time function α. By ‘gauge-transformation of the second kind’ we understand a transformation of the type ϕk→ϕk−i(∂α/∂xk)/ε as for those of the electromagnetic potentials.

the offending part is here:
U→Ue^{iα}U→Ue^{—iα} (I have added the curly brackets to denote the argument of the exponential, omitted above and below)

to get the physics right, it needs to be:
U→Ueiα, U→Ue—iα

the offending part is wrong because, as shown online, U (a tensor or spinor) is said to 'go' to something of a very different abstract dimension, UU*, the complex scalar notwithstanding. This is wrong, not something a gauge transformation would do I think. A comma and a space would restore the original meaning of Pauli's.

It's really understandable how the error seems to have crept in. The quote comes not from the body of the paper but a footnote on page 718 of the reference (OCTOBER 15, 1940 Physical Review
VOLUME 58 `The Connection Between Spin and Statistics', etc.).

Pauli has a space between the 2 separate species of the gauge transformation of the first kind, and the OED simply omits the space, but as it is a mathematical expression, omission of the space makes for the mathematical error, which does not exist in Pauli's paper, but does exist in the OED.

Putting in the comma (and restoring the space) would be best. I do not know if there exists a phrase like [our. punct.] or something to indicate that Pauli's original expression could've been improved upon.

I would like to submit this note in hopes of eventually there being a remedy in the OED.


  • Hi @gdsevernUSA

    Many thanks for flagging this up to our attention.

    I will forward this internally to the right people for their consideration.
    Please note that I might not be able to get back to you with any outcomes, as the editors have a high volume of suggestions to review, so they are not able to reply individually to the people who submit them (that also means it may take them some time to be able to look into the point you raised).

    And if you notice anything else that doesn't seem right, let us know!

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