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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A corresponding extension of the large-order perturbation theory now also applies to small orders. Photo taken in Chervyakov, Kleinert developed an extension of the theory of distributions from kleunert spaces to semigroups by defining their products uniquely in the mathematical theory, only linear combinations are defined.

Annemarie Kleinert since with whom he has a son Michael Kleinert. Kleinert’s 60th birthday was honored by a Festschrift and a Festcolloquium with 65 contributions by international colleagues for instance Y.

pxth At the summer school in Erice he proposed the existence of broken supersymmetry in atomic nuclei, [15] which has since been observed experimentally. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely products of distributions. By using this site, you agree to the Terms of Use and Privacy Policy.

Kleinert earned his doctorate in at the University of Colorado, Boulder. In this theory, the statistical properties of fluctuating vortex or defect lines are described as elementary excitations with the help of fields, whose Feynman diagrams are the pictures of the lines.

This curvature reproduces all the effects of kleniert relativitybut leads to different physics than string theory at the scale of the Planck length. This theory inspired Italian artist Laura Pesce to create glass sculptures inetgrals “world crystal” see also lower left on this page.

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. A variational treatment extends the range of validity to small barriers. 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.

Views Read Edit View history. The solutions have been made possible by two major advances. Tunneling intergals 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.

## Hagen Kleinert

He studied physics at the University of Hanover between andand at several American universities including Georgia Institute of Technologywhere he learned general relativity as a graduate student from George Gamowone of the fathers of the Big Bang theory.

Hagen Kleinert Limited preview – Inhe considered the existence of a novel Riemann particle. In he introduced [20] stiffness into the theory of stringswhich had formerly been characterized by tension alone. This page was last edited on 28 Septemberat This so-called variational perturbation theory yields at present the most accurate theory of critical exponents [7] observable close to second-order phase transitionsas confirmed for superfluid helium in satellite experiments.

### Homepage of Hagen Kleinert

For his contributions to particle and solid state physics he was awarded the Max Born Prize with Medal. Kleinert is a senior member of the faculty for the International Relativistic Astrophysics Ph. 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.

The experimental verification is still missing. 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.

Max Born Prize Majorana Prize This is the fifth, expanded edition of the comprehensive textbook published in on the theory and applications of path integrals.

### Hagen Kleinert – Wikipedia

Free University of Berlin. Devreeseand K. Please help improve it by revising it to be neutral and encyclopedic. Polyakov intevrals proposed a similar extension, and so the model is now known as the Polyakov-Kleinert string.

The convergence is uniform from weak to strong couplings, opening a way to precise evaluations of analytically unsolvable path integrals in the strong-coupling regime where they describe critical phenomena.

In this model, matter creates defects in spacetime which generate curvature. Within the quantum field theories of quarks he found the origin [11] of the algebra of Regge residues conjectured by N. Retrieved from ” https: