Günter Scharf

Prof. Dr. Günter Scharf (*September 19,1938, Nordhausen, Germany)
was my doctoral adviser at the University of Zürich.

Günter Scharf finished his Ph.D. thesis "Fastperiodische Potentiale" in 1965 under the supervision of Prof. Dr. Armin Thellung (1924-2003, see the picture below), who was one of the last Ph.D. students of Wolfgang Pauli.

Günter Scharf has written three books:

1) "Finite Quantum Electrodynamics" (Springer, 1989/1995), in which he shows how one can avoid ultraviolet divergences in QED by making use of causality and distribution theory.

2) "Quantum Gauge Theories : A True Ghost Story" (Wiley, 2001) extends the causal method to gauge theories.

3) "From Electrostatics to Optics" (Springer, 1994), an excellent textbook containing a concise introduction to classical electrodynamics.

The causal approach to quantum field theory advocated during the last 20 years by Scharf goes back to a classic paper by H. Epstein and V. Glaser. The method has the great advantage that it uses mathematically well-defined objects only, namely free asymptotic fields. Therefore all mathematical operations have a precise meaning in the framework of distribution theory, in particular, there are no ultraviolet divergences. The method has been applied to abelian, massless non-abelian and to massive non-abelian gauge theories. In the latter case one obtains the complete structure of the standard electroweak theory as a consequence of (quantum) gauge invariance, without using spontaneous symmetry breaking. In the case of spin-2 gauge fields gauge invariance alone leads to the same couplings as given by Einstein's theory (see also G.Scharf, Quantum gauge theories - a true ghost story). The extension of the method to supersymmetry and Georgi-Glashow SU(5) is also under study. It turns out that supergauge theories can be constructed
by the causal method in close analogy to ordinary quantum gauge theory.



First person on the right: Prof. Dr. Armin Thellung.
On the left: Prof. Dr. Norbert Straumann, Prof. Dr. Günter Rasche (and others).