Markus Fierz, professor emeritus of theoretical physics at the ETH Zürich, died peacefully on June 20, 2006, his 94th anniversary, after a rich, harmonious life. Although he had been increasingly fragile, he had retained a phenomenal memory and a mental serenity and grace that impressed all his visitors, almost up to his end. Fierz made significant contributions to relativistic quantum field theory and to general relativity, the most important new theories of physics in his younger days.
Born 1912 in Basel, Switzerland, Fierz went to the University of Göttingen in 1931 to study physics and biology. There he enjoyed the inspiring lectures of Hermann Weyl and studied the works of Immanuel Kant. After the Nazis came to power Fierz returned to Zürich, in 1933, to major in physics under the guidance of Gregor Wentzel (University of Zürich) and Wolfgang Pauli (ETH).
In his 1936 dissertation with Wentzel, he discovered the 'infrared catastrophe' in the description of scattering processes of relativistic charged particles. He found a divergent scattering cross-section in lowest non-trivial order due to the emission of soft photons. In 1938, inspired by the work of Bloch and Nordsieck, Pauli and Fierz studied the 'Pauli-Fierz model' of a nonrelativistic electron coupled to the radiation field. This exactly solved model has scattering states that carry a representation of the canonical commutation relations inequivalent to the Fock representation. The infrared divergencies occur in an unjustified perturbative expansion. Fierz spent the summer term of 1936 at the institute of Werner Heisenberg in Leipzig, but then he returned to Zürich to become Pauli's assistant.
In 1937, in his work on Fermi's theory of beta decay, Fierz succeeded to reduce the number of invariant matrix elements without derivative couplings to five using the so-called 'Fierz transformations'. This allowed him to compute the beta spectra and neutron-proton forces for a general linear combination of the five invariants, a very elegant and modern approach.
Fierz' most important result was his proof of the general connection of spin and statistics of elementary particles, namely Bose-Einstein statistics for integer spin and Fermi-Dirac statistics for half-integer spin. For this pioneering work Fierz received the Max-Planck Medal in 1979. Later, these results were generalized to interacting fields satisfying the Wightman axioms of general quantum fields and are one of the pillars of particle physics. In joint work with Pauli he applied his methods to fields with electromagnetic interactions. Their results on the local gauge group of massless particles of spin 3/2 and 2 became important for supergravity.
From 1936 to 1940 Fierz was a research assistant with Wolfgang Pauli at ETH, then a "Privatdozent" till 1943. Between 1943 and 1959, he was professor in Basel to become the director of the Theory Division at CERN for one year. In 1950, in a beautiful paper, Fierz clarified the causality properties of the Stückelberg-Feynman propagator. Here the magic decomposition Dc = Dret + Dav inspired the work on renormalized perturbation theory of the younger generation. From 1960 until his retirement in1977, Fierz served as Pauli's successor at ETH. Together with his colleague and friend Res Jost he inspired the research, style and atmosphere at the Institute of Theoretical Physics, which at that time was a magnet with international attraction for all theoreticians with a taste for a mathematical description of physics. In 1989 Fierz was awarded the Einstein medal of the Albert-Einstein Society in Bern.
The thinking of Markus Fierz was strongly influenced by Wolfgang Pauli and Carl Gustav Jung. With both of them he was closely tied intellectually and by friendship. Due to their influence he gained his deep understanding of the two complementary worlds of physics and psychology. This understanding has inspired many essays, which, fortunately, have been published and show the rare understanding of their author.
In his later years, also after his retirement, Fierz has been intensely preoccupied with the history of science. His book on Girolamo Cardano leads into the center of the intellectual life, two generations before Galileo. It is a masterful tour through renaissance science, medicine and theology, bringing out the many interesting sides of this 'unfashionable' world, without the vanity of knowing better from a modern perspective. Fierz' ETH lecture notes on the history of mechanics were translated into Japanese. Fierz had an outstanding understanding of Newton's fundamental 'Principia', which in their original language and geometric reasoning are very difficult to understand for us contemporary physicists. Masterful are essays on the origin and significance of the concept of absolute space and on the early history of the Royal Society of London.
With his impressive knowledge, a sharp view of the essential points and with fine intuition Fierz thought and sensed the spirit and the importance of some of the greatest figures of our civilisation – Newton, Goethe and others – and placed their work into a more general context. Many of us remember, with deep gratitude, the illumination and friendship that Markus Fierz has given to us.
