Hagen Kleinert
Hagen Kleinert | |
|---|---|
 Photo taken in 2006 | |
| Born | 15 June 1941 |
| Died | 7 March 2025 (aged 83) |
| Alma mater | Technical University of Hanover Georgia Institute of Technology University of Colorado Boulder |
| Known for | Path integrals in polymer science World crystal Variational perturbation theory Duru–Kleinert transformation |
| Scientific career | |
| Fields | Theoretical physics |
| Institutions | Free University of Berlin |
Hagen Kleinert (15 June 1941 – 7 March 2025) was a professor of theoretical physics at the Free University of Berlin, Germany.[1]
Biography
[edit]Kleinert was born in Festenberg on 15 June 1941. Raised in Hanover, he graduated high school in 1960 and obtained his Vordiplom with distinction from the Technical University of Hanover in 1962.[1]
In 1963, Kleinert moved to the United States, earning a Master of Science degree from the Georgia Institute of Technology in 1964. After studying at several intermediate institutions, he obtained his PhD from the University of Colorado Boulder in 1967 under the supervision of Asim Barut.[1]
He then returned to Germany and joined Freie Universität Berlin, where he finished his habilitation and became an associate professor in 1969. Promoted to full professor in 1976, he worked there until retiring in 2009. He died on 7 March 2025.[1]
Research
[edit]Kleinert collaborated with Richard Feynman[2] in some of Feynman's final work, developing a method to approximate quantum-mechanical partition functions using classical distribution functions.[3][1] This led to variational perturbation theory, which enables a calculation of critical exponents[4] near second-order phase transitions. The result was later confirmed for the lambda point of helium in experiments conducted at zero gravity.[5]
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.[6][7][1]
Kleinert published over 400 articles, half of which were single-author papers.[1] 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.[8] He also wrote several review articles and multiple monographs.[9] His book on path integrals has become a standard reference work.[10][1]
Awards
[edit]In 2008, Kleinert received the Max Born Medal and Prize of the German Physical Society for his contributions to theoretical physics. The award recognized his work on path integrals and gauge field theories in both particle and condensed matter physics.[11]
On the occasion of his 60th birthday in 2001, a Festschrift titled Fluctuating Paths and Fields was dedicated to Kleinert.[12]
Books
[edit]- 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 ISBN 9971-5-0210-0 (also available online: Vol. I Archived 27 May 2008 at the Wayback Machine and Vol. II Archived 27 May 2008 at the Wayback Machine)
- Critical Properties of φ4-Theories, World Scientific (Singapore, 2001); Paperback ISBN 981-02-4658-7 (also available online Archived 16 July 2011 at the Wayback Machine) (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 Archived 1 January 2009 at the Wayback Machine)
- Multivalued Fields in Condensed Matter, Electrodynamics, and Gravitation, World Scientific (Singapore, 2008) (also available online Archived 18 March 2009 at the Wayback Machine)
- 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)
References
[edit]- 1 2 3 4 5 6 7 8 "Obituary for Hagen Kleinert". www.physik.fu-berlin.de. 28 August 2025. Retrieved 22 July 2026.
- ↑ Kleinert H. (2004). "Travailler avec Feynman" (PDF). Pour la Science. 19: 89–95. Archived from the original (PDF) on 26 November 2022. Retrieved 8 May 2009.
- ↑ Feynman R.P., Kleinert H. (1986). "Effective classical partition functions" (PDF). Physical Review A. 34 (6): 5080–5084. Bibcode:1986PhRvA..34.5080F. doi:10.1103/PhysRevA.34.5080. PMID 9897894. Archived from the original (PDF) on 12 March 2020. Retrieved 4 March 2008.
- ↑ Kleinert, H., "Critical exponents from seven-loop strong-coupling φ4 theory in three dimensions". Physical Review D 60, 085001 (1999)
- ↑ Lipa J.A.; Nissen, J.; Stricker, D.; Swanson, D.; Chui, T. (2003). "Specific heat of liquid helium in zero gravity very near the lambda point" (PDF). Physical Review B. 68 (17) 174518. arXiv:cond-mat/0310163. Bibcode:2003PhRvB..68q4518L. doi:10.1103/PhysRevB.68.174518. S2CID 55646571. Archived from the original (PDF) on 12 March 2020. Retrieved 4 March 2008.
- ↑ Duru I.H.; Kleinert H. (1979). "Solution of the path integral for the H-atom" (PDF). Physics Letters B. 84 (2): 185–188. Bibcode:1979PhLB...84..185D. doi:10.1016/0370-2693(79)90280-6. Archived from the original (PDF) on 9 March 2008. Retrieved 16 February 2005.
- ↑ Duru I.H.; Kleinert H. (1982). "Quantum Mechanics of H-Atom from Path Integrals" (PDF). Fortschr. Phys. 30 (2): 401–435. Bibcode:1982ForPh..30..401D. doi:10.1002/prop.19820300802. Archived from the original (PDF) on 27 June 2007. Retrieved 16 February 2005.
- ↑ Kleinert, Michael. "Homepage of Hagen Kleinert". users.physik.fu-berlin.de. Archived from the original on 6 December 2019. Retrieved 20 July 2026.
- ↑ Henry B.I. (2007). "Book Reviews". Australian Physics. 44 (3): 110. Archived from the original on 14 April 2020. Retrieved 8 February 2008.
- ↑ Kleinert, Hagen (2004). Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets (3rd ed.). World Scientific. doi:10.1142/5057. ISBN 978-981-238-106-4. Retrieved 22 July 2026.
- ↑ "Preisträgerinnen und Preisträger". DPG. Retrieved 22 July 2026.
- ↑ Janke, Wolfhard; Pelster, Axel; Schmidt, Hans-Jürgen; Bachmann, Michael, eds. (2001). Fluctuating Paths and Fields: Festschrift Dedicated to Hagen Kleinert on the Occasion of His 60th Birthday. Singapore: World Scientific. doi:10.1142/4726. ISBN 978-981-281-124-0.
