Hagen Kleinert (born 15 June ) is Professor of Theoretical Physics at the Free University of He also discovered an alternative to Feynman’s time-sliced path integral construction which can be used to solve the path integral formulations. Buy Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Polymer Physics, and Financial Markets by Hagen Kleinert Paperback $ Buy Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics, Hagen Kleinert is Professor of Physics at the Freie Universität Berlin, Germany.

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He studied physics at the University of Hanover between andand at several American universities including Georgia Institute of Technologywhere he learned general relativity as hagwn graduate student from George Gamowone of the fathers of the Big Bang theory. This so-called variational perturbation theory yields at present the most accurate theory of critical exponents [7] observable close to second-order integarls transitionsas confirmed for superfluid helium in satellite experiments.

Annemarie Kleinert since with whom he has a son Michael Kleinert. As an alternative to string theoryKleinert used the complete analogy between non-Euclidean geometry and the geometry of crystals with defects to construct a model of the universe called the World Crystal or Planck-Kleinert crystal. Lettere al Nuovo Cimento. This is haten fifth, expanded edition of the comprehensive textbook published in on the theory and applications of path integrals.

In this theory, the statistical properties of fluctuating vortex or defect lines are described as intsgrals excitations with the help of fields, whose Feynman diagrams are the pictures of the lines. Special attention is devoted to path integrals with topological restrictions needed to understand the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics.

In addition to the time-sliced definition, the author gives a perturbative, coordinate-independent definition of path integrals, which makes them invariant under coordinate transformations. For his contributions to particle and solid state physics he was awarded the Max Born Prize with Medal.

## Hagen Kleinert

Selected pages Title Page. The second is a new nonholonomic mapping principle carrying physical laws in flat spacetime to spacetimes with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations. Kleinert is a senior member of the faculty for the International Relativistic Astrophysics Ph.

Kleinert’s 60th birthday was honored by a Festschrift and a Festcolloquium with 65 contributions by international colleagues for instance Y. Later, Kleinert was to collaborate with Feynman [5] in some of the latter’s last work.

Max Born Prize Majorana Prize It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. His theory of collective quantum fields [17] and the Hadronization of Quark Theories [18] are prototypes for numerous developments in the theory of condensed matternuclear and elementary particle physics. The solutions have been made possible by two major advances.

The theory is based on a disorder field theory dual to the order field theory of L. Devreeseand K. Polyakov simultaneously proposed a similar extension, and so the model is now known as the Polyakov-Kleinert string.

### Hagen Kleinert – Wikipedia

My library Help Advanced Book Search. At the summer school in Erice he proposed the existence of broken supersymmetry in atomic nuclei, [15] which has since been observed experimentally. Kleinert earned his doctorate in at the University of Colorado, Boulder. Hagen Kleinert Limited preview – In this model, matter creates defects in spacetime which generate curvature.

In he introduced [20] stiffness into the theory of stringswhich had formerly been characterized by tension alone. Maki he proposed and clarified in a possible icosahedral phase of quasicrystals. Tunneling processes are treated in detail, with applications to the lifetimes of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions.

This theory inspired Italian artist Laura Pesce to create glass sculptures entitled “world crystal” see also lower left on this page. From Wikipedia, the free encyclopedia. George Gamow Richard Feynman.

Chervyakov, Kleinert developed an extension of the theory of distributions from linear spaces to semigroups by defining their products uniquely in the mathematical theory, only linear combinations are defined. A variational treatment extends the range of validity to small barriers.

This greatly improved the description of the physical properties of strings. This page was last edited on 28 Septemberat Within the quantum field theories of quarks he found the origin [11] of the algebra of Regge residues conjectured by N.

The powerful Feynman-Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent results. For superconductors he predicted in 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.

University of Hanover University of Colorado, Boulder. Account Options Sign in. Landau for phase transitions which Kleinert developed in the books on Gauge Fields in Condensed Matter. The experimental verification is still missing. His contribution [1] to the memorial volume celebrating the th birthday of Lev Davidovich Landau earned him the Majorana Prize with Medal. Views Read Edit View history. This curvature reproduces all the effects of general relativitybut leads to different physics than string theory at the scale of the Planck length.

He is married to Dr.

### Homepage of Hagen Kleinert

The Russian physicist A. By using this site, you agree to the Terms of Use and Privacy Policy.

Hagen Kleinert No preview available – Inhe considered the existence of a novel Riemann particle. Photo taken in Retrieved from ” https: