Hagen Kleinert

Hagen Kleinert (15 June 1941 – 7 March 2025) was a professor of theoretical physics at the Free University of Berlin, Germany. in some of Feynman's final work, developing a method to approximate quantum-mechanical partition functions using classical distribution functions. near second-order phase transitions. The result was later confirmed for the lambda point of helium in experiments conducted at zero gravity.

Together with İsmail Duru, Kleinert developed the Duru–Kleinert transformation, an alternative to Feynman's time-sliced path integral construction, which can be used to solve the path integral formulations of the hydrogen atom and the centrifugal barrier. The topics include mathematical physics and the physics of elementary particles, nuclei, solid state systems, liquid crystals, biomembranes, microemulsions, polymers, and the theory of financial markets. He also wrote several review articles and multiple monographs. His book on path integrals has become a standard reference work.

On the occasion of his 60th birthday in 2001, a Festschrift titled Fluctuating Paths and Fields was dedicated to Kleinert.

Books Gauge Fields in Condensed Matter, Vol. I, " SUPERFLOW AND VORTEX LINES", pp. 1–742, Vol. II, "STRESSES AND DEFECTS", pp. 743–1456, World Scientific (Singapore, 1989); Paperback (also available online: Vol. I and Vol. II ) Critical Properties of φ4-Theories, World Scientific (Singapore, 2001); Paperback (also available online ) (together with V. Schulte-Frohlinde) Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 5th edition, World Scientific (Singapore, 2009) (also available online ) Multivalued Fields in Condensed Matter, Electrodynamics, and Gravitation, World Scientific (Singapore, 2008) (also available online ) Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity, World Scientific (Singapore, 2008) (together with R.T. Jantzen) Particles and Quantum Fields, World Scientific (Singapore, 2016) (also available online)