Who is this "Kallen" and what does he represent, anyway?

1. csmallw

22
Hi all,

I'm working on a Green function chapter of my dissertation, am referencing the equation,

$$G(k,\omega) = \int_{-\infty}^\infty \frac{A(k,\omega')d\omega'}{\omega - \omega' + i0^+},$$

and I am trying to figure out the best way to credit it. I have noticed that condensed matter texts (Schrieffer, Mahan, for example) call it the "Lehmann" spectral representation, but Peskin and Schroeder and Wikipedia call it the "Kallen-Lehmann" spectral representation. Is there any reason I should not be also crediting Kallen for the formula above? The Peskin and Schroeder version of the equation (see p. 215) is slightly different from what I wrote above, but most of the differences seem like convention issues to me.

Thanks!

2. Simon Bridge

15,311
None. It's up to you.

Generally you should cite your source and label the equation only if you intend to refer to it by that label. If you want to name the equation, then it is appropriate to use the name most closely associated with the use you intend for the equation and the conventions of the journal the article is to appear in.

Usually you want to name an equation after someone if, by doing so, you are calling to the readers mind the justification for choosing that particular approach. Saves having to site a primary source, which may be many decades old, sometimes. So you use the name that will most have that effect on the reader.

Like we say "Newton's Laws" even though, arguably, Galileo should get primary credit because that is how people remember them and it means we don't have to cite Principia directly: everyone knows already.

If you don't care about that, don't bother. It sounds like you only concern is credit-where-credit's-due.

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3. king vitamin

210
This is really a history question, but I have to admit that it kind of interests me as well. I always find the different terms given to the same objects in CMT and HET interesting. I looked in Weinberg's QFT text, and he calls is Källen-Lehman and cites two papers:

G. Källen Helv. Phys. Acta 25, 417 (1952)
H. Lehmann Nuevo Cimento 11, 342 (1954)

as well as a QED textbook by Källen from the 1970s. In contrast, in Abrikosov, Dzyaloshinskii and Gor'kov's famous condensed matter textbook from the early 1960s only cites Lehmann's paper, and claims that equations of your kind were "first obtained by Lehmann in a paper on quantum field theory." I wonder why Källen doesn't get recognition there. Maybe some condensed matter physicists who did early work on Green's functions in CMT just didn't see the work, or maybe they deal with the problem in different ways such that CM theorists didn't think it relevant, or some other reason.

If you really think you need to cite a source for the spectral representation, just cite Mahan or whoever your favorite textbook is. However, you could probably get away with just presenting this "common knowledge" unless your paper specifically deals with the properties of Green's functions in general.

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4. csmallw

22
Thanks! Both these responses were helpful.