  Feynman diagrams are a pictorial way of describing integrals predicting
possible outcomes of interactions of subatomic particles in the context of
quantum field physics. It is highly desirable to have an intrinsic mathematical
interpretation of Feynman diagrams, and in this article we find the
representation-theoretic meaning of a particular kind of Feynman diagrams
called the two-loop ladder diagram. This is done in the context of
representations of a Lie group U(2,2), its Lie algebra u(2,2) and quaternionic
analysis. The results and techniques developed in this article are used in [L]
to provide a mathematical interpretation of all conformal four-point integrals
- including those described by the n-loop ladder diagrams - in the context of
representations U(2,2) and quaternionic analysis. Moreover, this
representation-quaternionic model produces a proof of "magic identities" in the
Minkowski metric space.
  No prior knowledge of physics or Feynman diagrams is assumed from the reader.
We provide a summary of all relevant results from quaternionic analysis to make
the article self-contained.
