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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This curvature reproduces all the effects of general relativitybut leads to different physics than string hagsn at the scale of the Planck length.

### Homepage of Hagen Kleinert

Max Born Prize Majorana Prize Account Options Sign in. From Wikipedia, the free encyclopedia.

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. University of Hanover University of Colorado, Boulder. Inhe considered the existence of a novel Riemann particle. My library Help Advanced Book Search.

The Russian physicist A. 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. 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 pathh.

## Hagen Kleinert

In he introduced [20] stiffness into the theory of stringswhich had formerly been characterized by tension alone. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom.

The theory is based on a disorder field theory dual to the order field theory of L.

Landau for phase transitions which Kleinert developed in the books on Gauge Fields in Condensed Matter. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely products integraals distributions.

Integfals University of Berlin. Hagen Kleinert No preview available – 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.

George Gamow Richard Feynman.

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. This page was last edited on 28 Septemberat 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.

By using this site, you agree to the Terms of Use and Privacy Policy. This theory inspired Italian artist Laura Pesce to create glass sculptures entitled “world crystal” see also lower left on this page.

Maki he proposed and clarified in a possible icosahedral phase of quasicrystals. A corresponding extension of the large-order perturbation theory now also applies to small orders. Polyakov simultaneously proposed a similar extension, and so the model is now known as the Polyakov-Kleinert string. 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.

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.

The solutions have been made possible by two major advances. Hagen Kleinert Limited preview – Please help improve it by revising it to be neutral and encyclopedic. 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.

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.

Selected pages Title Page. The experimental verification is still missing. Later, Kleinert was to collaborate with Feynman [5] in some of the latter’s last work.