## On Stapp's Theorem

### Peter Minkowski, David N. Williams

and

Rudolf Seiler

Institüt für Theoretische Physik

Eidgenössische Technische Hochschule

Zürich, 1964
**Abstract:**
Stapp's Theorem says that the complex domain of regularity of a
function holomorphic on a real domain of several four-vectors,
perhaps restricted to the mass shell, and covariant under the
connected component of the real homogeneous Lorentz group, is a
union of invariant sheets consisting of orbits under the
connected component of the complex, homogenous Lorentz group,
under which the function is complex covariant. The original
proof used a local connectedness property of complex orbits. R.
Jost found a counterexample for certain points of degenerate
dimension, which invalidated the proof there.

Two of us provide independent proofs that the theorem is
nevertheless true at such points, based on a weaker
connectedness property, and one of us shows that Jost's
counterexample characterizes the points where strong local
connectedness fails. Finally, we point out that the proof of
the theorem extends to the complex classical groups of any
finite dimension GL(n,C), SL(n,C), and O_{+}(n,C).
Possibly it works for Sp(n,C), but the weaker connectedness
property remains to be checked in that case.

Published in *Lectures in Theoretical Physics*, vol. VII A,
*Lorentz Group*, (University of Colorado Press, Boulder,
1965), pp. 173–189.

Back to webprints

Back to home page.