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

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In summary, there is no reason not to credit Kallen for the formula mentioned in the conversation. It is up to the writer's discretion whether to name the equation after someone or not, as long as proper credit is given. The different terms used in condensed matter and high energy theories may be due to various factors such as historical context or differences in approach. It is also possible to present the equation as common knowledge without specifically citing a source.
  • #1
csmallw
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Hi all,

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

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

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!
 
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  • #2
csmallw said:
Is there any reason I should not be also crediting Kallen for the formula above?
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.

i.e. your labels can double for communication, adding meta-data and historical context to your arguments.
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
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
Thanks! Both these responses were helpful.
 

1. Who is this "Kallen" and why is he important in science?

Kallen is not a specific person, but rather a term used in sociology and political science to refer to the collective group of individuals who have similar social and political ideologies. In science, Kallen may be referenced when discussing the impact of groupthink on scientific research or when studying the effects of group dynamics on decision making in scientific teams.

2. What is the significance of Kallen in the scientific community?

The concept of Kallen is important in the scientific community as it highlights the influence of group dynamics and social factors on the process and outcomes of scientific research. It also reminds scientists to critically evaluate their own biases and the potential impact of groupthink in their work.

3. How does the idea of Kallen relate to diversity and inclusion in science?

The concept of Kallen highlights the importance of diversity and inclusion in science. When individuals with different backgrounds, perspectives, and ideologies come together to form a group, it can lead to more innovative and unbiased research. This can help counteract the negative effects of groupthink and promote a more inclusive scientific community.

4. Is Kallen a new concept in science?

No, the concept of Kallen has been around for decades, first introduced by the American philosopher and sociologist, Horace Kallen, in 1915. However, it is still a relevant and important concept in modern science as it continues to be studied and discussed in relation to group dynamics and social influences on scientific research.

5. How can researchers avoid the negative effects of Kallen in their work?

To avoid the negative effects of Kallen, researchers should actively seek out diverse perspectives and backgrounds in their teams, encourage open and critical discussions, and continuously reflect on their own biases and potential groupthink. Additionally, creating a culture of inclusivity and respect within the scientific community can help promote diverse and unbiased research.

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