For some reason, everybody refers to the function $$\lambda(x,y,z) = x^2 + y^2 + z^2 - 2xy -2xz-2yz$$ as "Källén's triangle function." (see for example https://en.wikipedia.org/wiki/Gunnar_Källén). I understand why its a triangle function (because it's proportional the area of a triangle of sides $x$ $y$ and $z$).

But how did Källén get his name attached to it? Is there a paper of his where he used that combination a lot?

  • $\begingroup$ The Wikipedia article states that the function appears in several kinematic equations, which Kallen presumably studied. $\endgroup$
    – HDE 226868
    Dec 24, 2015 at 13:40
  • $\begingroup$ @HDE226868 Thanks, I already know that (by reading the article). Would you know which equations in particular he studied, and the papers in which he studied them? $\endgroup$
    – QuantumDot
    Dec 24, 2015 at 20:26
  • $\begingroup$ Nope, not "everybody" calls that function by someone's name. I've never heard a name for this function before I read it here. $\endgroup$
    – KCd
    Dec 25, 2015 at 3:35
  • $\begingroup$ @KCd Thanks, that was exactly what I needed to know. $\endgroup$
    – QuantumDot
    Dec 25, 2015 at 11:44

1 Answer 1


In 1964 Källén wrote a textbook with the title "Elementary Particle Physics", which introduces the symbol with the words "The $\lambda(x,y,z)$ is a symbol which occurs frequently in this book."

In Wightman's obituary for Gunnar Källén (http://projecteuclid.org/euclid.cmp/1103841217), he states that "A typical remark about the book was: That is the book on elementary particles the experimentalists really find helpful", which might indicate a certain popularity of the book.

This gives one possible answer to your question.


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