Hagen Kleinert

Hagen Kleinert Michael (born 15 June 1941 in Festenberg ) is a German physicist and professor of theoretical physics at the Free University of Berlin.

Kleinert studied 1960-1963 Physics at the Technical University of Hanover, afterwards at several universities in the United States. In 1967 he received his doctorate from the University of Colorado at Boulder, where he among other things, studied with George Gamow, one of the fathers of the Big Bang theory. Since 1969 he is professor at the Free University of Berlin.


In collaboration with Richard Feynman, he developed an approximate method for the calculation of path integrals. This has been expanded in the last 15 years to a mathematical method, with which can be converted into convergent power series divergent. This method is based on the present ( 2008) the most accurate theory of critical exponents, which can be observed in the vicinity of phase transitions of second order. In particular, this theory for superfluid helium said measured in a satellite experiment results require accurate.

Using the quark field theory in 1973, he found the explanation of the presumed by Nicola Cabibbo, L. Horwitz and Yuval Ne'eman algebra of Regge couplings.

His theory of collective quantum fields and the hadronization of quark theories were used as templates for many developments in the theory of condensed matter, nuclear and elementary particle physics.

On a summer school in Erice he proposed in 1978 before the existence of supersymmetry in atomic nuclei, which was found experimentally in the meantime.

Together with H. Duru he broke 1979 for the first time the path integral of the hydrogen atom.

Together with K. Maki 1981, he clarified the structure of the icosahedral phase of quasicrystals on. For superconductors in 1982 he said ahead of a between type I and type II located tricritical point in the phase diagram, which was confirmed by Monte Carlo simulations. The prediction is based on a new disorder field theory, which he developed in the two books on Gauge Fields in Condensed Matter ( see below). This fluctuating vortex - or defect lines are described as elementary excitations with the help of fields. This is a dual version of the landau is order field theories for phase transitions.

In 1986, he led the bending stiffness in the string theory in which normally only voltages play a role. This makes it substantially improved the physical properties of the strings. As the Russian physicist Alexander Polyakov about the same time proposed a similar theory, the result is called Polyakov - Kleinert string also.

From Koordinateninvarianz of path integrals he derived an extension of the theory of distributions, are clearly defined in the not only (as in the mathematical theory of distributions ), linear combinations but also products of distributions. The Koordinateninvarianz is a necessary property of path integrals, so that they are equivalent to the Schrödinger picture of quantum mechanics.


  • Dr. Kleinert is H.C. at the University of the West Timişoara and at the Kyrgyz- Russian Slavic University in Bishkek.
  • He is an honorary member of the Russian International Academy of Creative Endeavors.
  • In 2008 he was awarded the Max Born Prize with medal.
  • His contribution to the memory band for the 100th anniversary of Lev Davidovich Landau was the Electronic Journal of Theoretical Physics awarded the Majorana Medal 2008.
  • His 60th birthday was honored with a Festkolloquim and a Festschrift to the 65 colleagues (including Juval Ne'eman, Roman Jackiw, Harald Fritzsch, Remo Ruffini, Cécile DeWitt - Morette, Louis H. Kauffman, Jozef T. Devreese, Kazumi Maki, ...) contributing.


  • Gauge Fields in Condensed Matter. Volume I: Superflow and Vortex Lines; Disorder Fields, Phase Transitions. World Scientific, Singapore, 1989, ISBN 9971-5-0210-0 (online)
  • Gauge Fields in Condensed Matter. Volume II: stress and Defects; Differential Geometry, Crystal Melting. World Scientific, Singapore, 1989, ISBN 9971-5-0210-0 (online)
  • Path integrals in Quantum Mechanics, Statistics, and Polymer Physics. World Scientific, Singapore, 1990, 2nd edition, World Scientific, Singapore, 1995
  • Path integrals in quantum mechanics, statistics and polymer physics. Mannheim 1993
  • With Verena Schulte- Frohlind: Critical Properties of φ4 - Theories. World Scientific, Singapore, 2001, ISBN 981-02-4658-7 (online)
  • Path integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets. 5th edition, World Scientific, Singapore 2009 (online)
  • Multivalued Fields in Condensed Matter, Electrodynamics, and Gravitation. World Scientific, Singapore 2008 (online )
  • As editor with Robert T. Jantzen: Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity. World Scientific, Singapore 2008