Hagen Kleinert

Hagen Kleinert

Hagen Kleinert (born 1941) is Professor of Theoretical Physics at the Free University of Berlin, Germany (since 1968), Honorary Professor at the Kyrgyz-Russian Slavic University, and Honorary Member of the [http://www.physik.fu-berlin.de/~kleinert/news/academycreative.html Russian Academy of Creative Endeavors] . For his contributions to particle and solid state physics he was [http://www.iop.org/activity/awards/International_Bilateral_Awards/The_Max_Born_Medal_and_Prize/Born_medal_winners/page_29137.html awarded] the Max Born prize 2008 with [http://www.dpg-physik.de/dpg/preise/preistraeger/max-born-preis.pdf Medal] .

Kleinert has written more than 370 papers on mathematical physics and the physics of elementary particles, nuclei, solid state, liquid crystals, biomembranes, microemulsions, polymers, and theory of financial markets. He has written several books on theoretical physics. His most notable book "Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Market" has been published in four editions since 1990 with the latest two editions including chapters on the application of path integrals in financial markets. This book has received enthusiastic reviews [cite journal
title = Book Reviews
author = Henry B.I.
journal = Australian Physics
volume = 44
issue = 3
pages = 110
year = 2007
doi =
url = http://www.physik.fu-berlin.de/~kleinert/b5/reviews/picrithenry.doc
] .

After his first years as a student at Universität Hannover and Georgia Institute of Technology, he learned as a graduate student General Relativity from
George Gamov, one of the fathers of the Big Bang theory.As a young professor in 1972, Kleinert visited Caltech and was impressed by noted US physicist Richard Feynman. He discovered how to use Feynman's path integrals to solve the path integral of the hydrogen atom [cite journal
title = Solution of the path integral for the H-atom
author = Duru I.H., Kleinert H.
journal = Physics Letters B
volume = 84
issue = 2
pages = 185–188
year = 1979
doi = 10.1016/0370-2693(79)90280-6
url = http://www.physik.fu-berlin.de/~kleinert/kleiner_re65/65.pdf
] [cite journal
title = Quantum Mechanics of H-Atom from Path Integrals
author = Duru I.H., Kleinert H.
journal = Fortschr. Phys
volume = 30
issue = 2
pages = 401–435
year = 1982
doi =
url = http://www.physik.fu-berlin.de/~kleinert/kleiner_re83/83.pdf
] . This work greatly extended the applicable range of Feynman's techniques. Later, Kleinert was to collaborate with Feynman in some of the latter's last work [cite journal
title = Effective classical partition functions
author = Feynman R.P., Kleinert H.
journal = Physical Review
volume = A 34
issue =
pages = 5080–5084
year = 1986
doi = 10.1103/PhysRevA.34.5080
url = http://www.physik.fu-berlin.de/~kleinert/159/159.pdf
] .This has led to a mathematical method for converting divergent weak-coupling power series into convergent strong-coupling ones. This so-called variational perturbation theory yields at present the most accurate theory of critical exponents [
Kleinert, H., [http://www.physik.fu-berlin.de/~kleinert/279/279.pdf "Critical exponents from seven-loop strong-coupling φ4 theory in three dimensions". Physical Review D 60, 085001 (1999)]
] observable close to second-order phase transitions, as confirmed for superfluid helium in satellite experiments [cite journal
title = Specific heat of liquid helium in zero gravity very near the lambda point
author = Lipa J.A.
journal = Physical Review
volume = B 68
issue =
pages = 174518
year = 2003
doi = 10.1103/PhysRevB.68.1745
url = http://www.physik.fu-berlin.de/~kleinert/papers/lipa.pdf
doi_brokendate = 2008-06-22
] .

Within the quantum field theories of quarkshe found the origin [cite journal
title = Bilocal Form Factors and Regge Couplings
author = Kleinert H.
journal = Nucl. Physics
volume = B65
pages = 77–111
year = 1973
doi = 10.1016/0550-3213(73)90276-9
url = http://www.physik.fu-berlin.de/~kleinert/45/45.pdf
] of the [http://www.physik.fu-berlin.de/~kleinert/papers/chn.pdf algebra of Regge residues] conjectured by N. Cabibbo, L. Horwitz, and
Y. Ne'eman (see [http://www.physik.fu-berlin.de/~kleinert/papers/neeman1.pdf p.232] in Ref. [cite journal
title = Universality in the Algebra of Vertex Strengths as Generated by Bilocal Currents
author = Ne'eman Y, Reddy V.T.N.
journal = Nucl. Phys.
volume = B 84
pages = 221–233
year = 1981
doi = 10.1016/0550-3213(75)90547-7
url = http://www.physik.fu-berlin.de/~kleinert/papers/neemredd.pdf
] ).

Together with K. Maki he clarified the structure of the icosahedral phase of quasicrystals [cite journal
title = Lattice Textures in Cholesteric Liquid Crystals
author = Kleinert H., Maki K.
journal = Fortschritte der Physik
volume = 29
pages = 219–259
year = 1981
doi =
url = http://www.physik.fu-berlin.de/~kleinert/75/75.pdf
] .

For superconductors he predicted in 1982 a tricritical point in the phase diagram between type-I and type-II superconductors where the order of the transition changes from second to first [cite journal
title = Disorder Version of the Abelian Higgs Model and the Order of the Superconductive Phase Transition
author = Kleinert H.
journal = Lett. Nuovo Cimento
volume = 35
pages = 405–412
year = 1982
doi =
url = http://www.physik.fu-berlin.de/~kleinert/97/97.pdf
] . The predictions were confirmed in 2002 by Monte Carlo computer simulations [cite journal
title = Vortex interactions and thermally induced crossover from type-I to type-II superconductivity
author = Hove J., Mo S., Sudbo A.
journal = Phys. Rev.
volume = B 66
pages = 064524
year = 2002
doi = 10.1103/PhysRevB.66.064524
url = http://www.physik.fu-berlin.de/~kleinert/papers/sudbotre064524.pdf
] .

The theory is based on a new disorder field theory, which Kleinert developed in the books on "Gauge Fields in Condensed Matter " (see below). In this theory, the statistical properties of fluctuating vortex or defect lines are described as elementary excitations with the help pf fields, whose Feynman diagrams are the pictures of the lines.The disorder field theory is a dual version of the order field theory of L.D. Landau for phase transitions.

At the 1978 summer school in Erice he proposed the existence of broken supersymmetry in atomic nuclei [cite journal
title = The New Aspects of Subnuclear Physics
author = Ferrara S., Discussion Section of 1978 Erice Lecture publ. in
journal = Plenum Press, N.Y., Zichichi A. ed.
volume =
pages = 40
year = 1980
doi =
url = http://www.physik.fu-berlin.de/~kleinert/55/1978/supersnuc.pdf
] , which has meanwhile been observed experimentally [cite journal
title = Evidence for the Existence of Supersymmetry in Atomic Nuclei
author = Metz A., Jolie J., Graw G., Hertenberger R., Gröger J., Günther C., Warr N., Eisermann Y.
journal = Phys. Rev. Lett.
volume = 83
pages = 1542
year = 1999
doi = 10.1103/PhysRevLett.83.1542
url = http://prola.aps.org/pdf/PRL/v83/i8/p1542_1
] .

His theory of collective quantum fields [cite journal
title = Collective Quantum Fields
author = Kleinert H.
journal = Fortschritte der Physik
volume = 36
pages = 565–671
year = 1978
doi =
url = http://www.physik.fu-berlin.de/~kleinert/55/55.pdf
] and the Hadronization of Quark Theories [cite journal
title = On the Hadronization of Quark Theories
author = Kleinert H., Lectures presented at the Erice Summer Institute 1976
journal = Understanding the Fundamental Constituents of Matter, Plenum Press, New York, 1978 (A. Zichichi ed.)
volume =
pages = pp. 289–390
year = 1978
doi =
url = http://www.physik.fu-berlin.de/~kleinert/53/53.pdf
] are prototypes for numerous developments in the theory of condensed matter, nuclear and elementary particle physics.

In 1986 he introduced [cite journal
title = The Membrane Properties of Condensing Strings
author = Kleinert H.
journal = Phys. Lett. B
volume = 174
issue =
pages = 335
year = 1989
doi = 10.1016/0370-2693(86)91111-1
url = http://www.physik.fu-berlin.de/~kleinert/149/149.pdf
] stiffness into the theory of strings,which normally possess only tension. In this way he greatly improved the physical properties of strings. Since the Russian physicist A. Polyakovproposed simultaneously a similar extension, the result is called the [http://prola.aps.org/abstract/PRD/v41/i8/p2634_1 Polyakov-Kleinert string] .

Together with A. Chervyakov developed an extension of the theory of distributions from linear spaces to semigroups by defining also their products uniquely (in the mathematical theory, only linear combinations are defined). The extension became possible by the physical requirement that the path integrals must be invariant under coordinate transformations [cite journal
title =Rules for integrals over products of distributions from coordinate independence of path integrals
author = Kleinert H., Chervyakov A.
journal = Europ. Phys. J.
volume = C 19
issue =
pages = 743–747
year = 2001
doi = 10.1007/s100520100600
url = http://www.physik.fu-berlin.de/~kleinert/kleiner_re303/wardepl.pdf
] . This property is necessary for the equivalence of the path integral formulation to Schrödinger theory.

As an alternative to string theory, Kleinert used the complete analogy between non-Euclidean geometry and the geometry of crystals with defects to construct a model of the universe called
World Crystal or [http://www.physik.fu-berlin.de/~kleinert/papers/planckklcZN.pdf Planck-Kleinert crystal] which has, at distances of the Planck length, quite a different physics than string theory. In this model, matter creates defects in spacetime which generate curvature and all the effects of general relativity. This theory inspired Italian artist [http://www.laurapesce.it/ Laura Pesce] to create glass sculptures entitled [http://www.laurapesce.it/main/exhibitions/DICE2006/DICE2006.html "world crystal"] (see also lower left on [http://www.laurapesce.it/main/exhibitions/ArteScienza/ArteScienza.html this page] ).

Kleinert is a senior member of the faculty for the International Relativistic Astrophysics Ph.D. [http://www.icra.it/IRAPPhD/2007/Welcome.htm (IRAP)] Project, which forms part of the internationalö network for astrophysics [http://www.icra.it/Icranet/|ICRANet] . He was also involved in the European Science Foundation's project [http://www.esf.org/activities/research-networking-programmes/physical-and-engineering-sciences-pesc/current-research-networking-programmes/cosmology-in-the-laboratory-coslab.html Cosmology in the Laboratory] .



* "Gauge Fields in Condensed Matter", Vol. I, " SUPERFLOW AND VORTEX LINES", pp. 1--742, Vol. II, "STRESSES AND DEFECTS", pp. 743-1456, [http://www.worldscibooks.com/physics/0356.htm World Scientific (Singapore, 1989)] ; Paperback ISBN 9971-5-0210-0 " (also available online: [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents1.html Vol. I] and [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents2.html Vol. II] )"

* "Critical Properties of φ4-Theories", [http://www.worldscibooks.com/physics/4733.html World Scientific (Singapore, 2001)] ; Paperback ISBN 981-02-4658-7" (also available [http://www.physik.fu-berlin.de/~kleinert/b8 online] ) (together with V. Schulte-Frohlinde)"

* "Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets", 4th edition, [http://www.worldscibooks.com/physics/6223.html World Scientific (Singapore, 2006)] (also available [http://www.physik.fu-berlin.de/~kleinert/re.html#B8 online] )

* "Multivalued Fields in in Condensed Matter, Electrodynamics, and Gravitation", [http://www.worldscibooks.com/physics/6742.html World Scientific (Singapore, 2008)] (also available [http://www.physik.fu-berlin.de/~kleinert/re.html#B9 online] )

* "Proceedings of the [http://www.icra.it/MG/mg11 Eleventh Marcel Grossmann Meeting] on General Relativity", [http://www.worldscibooks.com/physics/6997.html World Scientific (Singapore, 2008)] (together with R.T. Jantzen)"

External links

* [http://www.physik.fu-berlin.de/~kleinert/ Personal homepage]

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