Hagen Kleinert was born on June 15, 1941, in Festenberg near Breslau, grew up in Hannover, graduated from high school there in 1960, and then studied at the Technical University of Hannover, where he passed the intermediate physics examination (Vordiplom) with distinction in 1962. In 1963 he went to the United States, first to the Georgia Institute of Technology in Atlanta, where he earned a Master of Science degree in 1964, and then, after several intermediate stations, to the University of Colorado, Boulder, where he received his PhD under Asim Barut in 1967. A little later he returned to Germany, completed his habilitation at Freie Universität Berlin in 1969, and in the same year was appointed associate professor. After declining two offers from other universities, he was appointed full professor in 1976 and held this position until his retirement in 2009.

Although Kleinert was originally rooted in elementary particle physics, his oeuvre extends far beyond that. His research topics ranged from the hydrogen atom to gravitation and from melting theories to financial market fluctuations. If one seeks an overarching theme, it can be found in the title of the beautiful and informative Festschrift for his 60th birthday: Fluctuating Paths and Fields. His dissertation and many subsequent publications stand somewhat apart, as he dealt with dynamical symmetry groups of the hydrogen atom and elementary particles, as well as with Regge theory, to which he made a number of important contributions. Later, however, he showed how to introduce collective fields via path integrals, for instance for pairs of particles, which could be applied to hadrons as well as to superconductors or superfluid helium-3. And in 1978, together with his Turkish postdoc, Ismail Duru, he succeeded in treating the hydrogen atom with path integrals. The proposal had originally come from Richard Feynman, with whom he also developed a highly accurate method for approximating quantum-mechanical partition functions using classical distribution functions. This became his most cited work, and he later gave a detailed account of their collaboration. The so-called variational perturbation theory, which allows the resummation of divergent perturbation series, has its roots here. In the case of the Phi⁴ theory, this led to extremely precise values for the critical exponents and a comprehensive book co-authored with his student Verena Schulte-Frohlinde. Other studies dealt with the properties of real membranes, a topic that was also experimentally investigated in the department in Wolfgang Helfrich’s group, as well as with the membrane properties of condensing strings. Many further topics can be found on his homepage.

All this resulted in around 400 publications, half of them single-authored and typically in letter format. From the very beginning, however, his output also included didactically very well-written review articles, and from the 1990s onward, extensive monographs. Among these, his book on path integrals became a standard reference work, bringing him widespread recognition. Other books deal with the aforementioned collective fields or with gauge fields describing vortices and defect lines. When he received the Max Born Prize in 2008 from both the German Physical Society and the British Institute of Physics, the citation praised him “for his many outstanding contributions to theoretical physics, in particular to the theory of path integrals and gauge field theories in elementary particle physics and in condensed matter physics.”

Hagen Kleinert could be both highly inspiring and quite challenging. He was extremely spontaneous, very quick, and technically extraordinarily strong. He could derive many things in his head and contribute an enormous background knowledge in discussions. From the outset, he was energetic, brought people into the department, and always had a group of guests and collaborators around him, while supervising about a dozen PhD theses. He was not involved in collaborative research centers, however, since he did not want to commit himself for many years, and he also had no long-term program of his own. Rather, he looked for problems that he found interesting and that he might be able to address with his methods. He had a tendency to compete with others, and it was important to him to be clearly visible internationally. That was certainly the case: he gave many lectures at conferences and summer schools, organized a major meeting on general relativity at Freie Universität Berlin in 2006, and was on friendly terms with a number of very renowned physicists such as Murray Gell-Mann, Gerard ’t Hooft, Yuval Ne’eman, and Kazumi Maki.

Hagen Kleinert’s interests did not end with physics. He spoke several languages, including Italian, had a strong affinity for that country, and, when in the right mood, also sang arias from Italian operas. With his passing, the Department of Physics has lost a distinctive personality who contributed significantly to its scientific profile and leaves behind a profound gap.

Ingo Peschel (Department of Physics), Wolfhard Janke (University of Leipzig), and Johannes Blümlein (DESY Zeuthen)