Hagen Kleinert

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Hagen Kleinert, Photo taken in 2006
Hagen Kleinert, Photo taken in 2006

Hagen Kleinert 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 Russian Academy of Creative Endeavors. For his contributions to particle and solid state physics he was awarded the Max Born prize 2008 with 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[1].

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[2][3]. 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[4]. 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[5] observable close to second-order phase transitions, as confirmed for superfluid helium in satellite experiments[6].

Within the quantum field theories of quarks he found the origin[7] of the algebra of Regge residues conjectured by N. Cabibbo, L. Horwitz, and Y. Ne'eman (see p.232 in Ref.[8]).

Together with K. Maki he clarified the structure of the icosahedral phase of quasicrystals[9].

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[10]. The predictions were confirmed in 2002 by Monte Carlo computer simulations[11].

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[12], which has meanwhile been observed experimentally[13].

His theory of collective quantum fields[14] and the Hadronization of Quark Theories[15] are prototypes for numerous developments in the theory of condensed matter, nuclear and elementary particle physics.

In 1986 he introduced[16] 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. Polyakov proposed simultaneously a similar extension, the result is called the 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[17]. 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 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 Laura Pesce to create glass sculptures entitled "world crystal" (see also lower left on this page).

Kleinert is a senior member of the faculty for the International Relativistic Astrophysics Ph.D. (IRAP) Project, which forms part of the internationalö network for astrophysics [1]. He was also involved in the European Science Foundation's project Cosmology in the Laboratory.

[edit] References

  1. ^ Henry B.I. (2007). "Book Reviews". Australian Physics 44 (3): 110. 
  2. ^ Duru I.H., Kleinert H. (1979). "Solution of the path integral for the H-atom". Physics Letters B 84 (2): 185-188. doi:10.1016/0370-2693(79)90280-6. 
  3. ^ Duru I.H., Kleinert H. (1982). "Quantum Mechanics of H-Atom from Path Integrals". Fortschr. Phys 30 (2): 401-435. 
  4. ^ Feynman R.P., Kleinert H. (1986). "Effective classical partition functions". Physical Review A 34: 5080-5084. doi:10.1103/PhysRevA.34.5080. 
  5. ^ Kleinert, H., "Critical exponents from seven-loop strong-coupling φ4 theory in three dimensions". Physical Review D 60, 085001 (1999)
  6. ^ Lipa J.A. (2003). "Specific heat of liquid helium in zero gravity very near the lambda point". Physical Review B 68: 174518. doi:10.1103/PhysRevB.68.1745. 
  7. ^ Kleinert H. (1973). "Bilocal Form Factors and Regge Couplings". Nucl. Physics B65: 77-111. doi:10.1016/0550-3213(73)90276-9. 
  8. ^ Ne'eman Y, Reddy V.T.N. (1981). "Universality in the Algebra of Vertex Strengths as Generated by Bilocal Currents". Nucl. Phys. B 84: 221-233. doi:10.1016/0550-3213(75)90547-7. 
  9. ^ Kleinert H., Maki K. (1981). "Lattice Textures in Cholesteric Liquid Crystals". Fortschritte der Physik 29: 219-259. 
  10. ^ Kleinert H. (1982). "Disorder Version of the Abelian Higgs Model and the Order of the Superconductive Phase Transition". Lett. Nuovo Cimento 35: 405-412. 
  11. ^ Hove J., Mo S., Sudbo A. (2002). "Vortex interactions and thermally induced crossover from type-I to type-II superconductivity". Phys. Rev. B 66: 064524. doi:10.1103/PhysRevB.66.064524. 
  12. ^ Ferrara S., Discussion Section of 1978 Erice Lecture publ. in (1980). "The New Aspects of Subnuclear Physics". Plenum Press, N.Y., Zichichi A. ed.: 40. 
  13. ^ Metz A., Jolie J., Graw G., Hertenberger R., Gröger J., Günther C., Warr N., Eisermann Y. (1999). "Evidence for the Existence of Supersymmetry in Atomic Nuclei". Phys. Rev. Lett. 83: 1542. doi:10.1103/PhysRevLett.83.1542. 
  14. ^ Kleinert H. (1978). "Collective Quantum Fields". Fortschritte der Physik 36: 565-671. 
  15. ^ Kleinert H., Lectures presented at the Erice Summer Institute 1976 (1978). "On the Hadronization of Quark Theories". Understanding the Fundamental Constituents of Matter, Plenum Press, New York, 1978 (A. Zichichi ed.): pp. 289-390. 
  16. ^ Kleinert H. (1989). "The Membrane Properties of Condensing Strings". Phys. Lett. B 174: 335. doi:10.1016/0370-2693(86)91111-1. 
  17. ^ Kleinert H., Chervyakov A. (2001). "Rules for integrals over products of distributions from coordinate independence of path integrals". Europ. Phys. J. C 19: 743-747. doi:10.1007/s100520100600. 

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