Hagen Kleinert

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Hagen Kleinert (15 June 1941 – 7 March 2025) was a German theoretical physicist and long-time professor at the Free University of Berlin. He made major contributions to path integrals, quantum mechanics, condensed matter physics, and particle theory. He authored about 420 papers and several influential books, including Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets.

Life and career
- Born in Festenberg (now Twardogóra, Poland) in 1941. He studied at Leibniz University Hannover (1960–63), spent time at Georgia Tech, and earned his PhD at the University of Colorado, Boulder in 1967. He visited Caltech in 1972 and worked with Richard Feynman.
- He helped develop variational perturbation theory, a method to turn divergent series into convergent ones, widely used to predict critical behavior near phase transitions.

Key contributions
- Duru–Kleinert transformation: a way to handle path integrals with singular potentials, such as the hydrogen atom.
- Polyakov–Kleinert string: added a stiffness term to string theory to better describe physical properties.
- World Crystal (Planck-Kleinert crystal): a model linking defects in spacetime to gravity, offering an alternative view to string theory.
- Co-development of the icosahedral phase of quasicrystals with Maki.
- Predicted a tricritical point in superconductors (between type-I and type-II) in 1982; later confirmed by computer simulations.
- Proposed broken supersymmetry in atomic nuclei at a 1978 summer school, which has since been explored experimentally.

Awards and honors
- Max Born Prize (2008) and Majorana Prize (2008).
- Honorary Doctorates from the West University of Timișoara and the Kyrgyz-Russian Slavic University.
- Honorary Member of the Russian Academy of Creative Endeavors.

Personal life and legacy
- Married to Annemarie Kleinert since 1974; they have a son, Michael.
- Kleinert’s work crossed mathematics and physics, influencing how scientists understand critical phenomena, quantum systems, and the nature of space, matter, and gravity.