Hij heeft het eredoctoraat mogen ontvangen van verschillende universiteiten en is Erelid van de Russische Academy of Creative Endeavors. Voor zijn bijdragen aan de deeltjesfysica en de fysica van vaste stoffen werd hem in de Max Born-Prijs toegekend en in datzelfde jaar ontving hij voor zijn bijdrage  aan het Volume ter ere van de ste verjaardag van Lev Davidovich Landau de Majorana Prijs Ook heeft hij verschillende wetenschappelijke boeken geschreven over Theoretische Fysica. Deze uitgave heeft zeer lovende kritieken ontvangen . Als jonge professor bezocht Kleinert in Caltech waar hij zeer onder de indruk raakte van Richard Feynman. Hier ontdekte hij hoe Feynmans Path Integrals toe te passen om het padintegraal van het waterstofatoom op te lossen  .
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Main Path integrals in quantum mechanics, statistics, polymer physics, and financial markets Path integrals in quantum mechanics, statistics, polymer physics, and financial markets Hagen Kleinert This is the fourth, expanded edition of the comprehensive textbook published in on the theory and applications of path integrals. 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 solutions have become possible by two major advances. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations.
In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions.
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 expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals. Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions.
A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders. Special attention is devoted to path integrals with topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics.
The Chern-Simons theory of particles with fractional statistics anyons is introduced and applied to explain the fractional quantum Hall effect.
The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions.
Path integrals in quantum mechanics, statistics, polymer physics, and financial markets
World Scientific , amazon. These properties are calculated for various second-order phase transitions of three-dimensional systems with high accuracy, in particular the critical exponents observable in experiments close to the phase transition. Beginning with an introduction to critical phenomena, this book develops the functional-integral description of quantum field theories, their perturbation expansions, and a method for finding recursively all Feynman diagrams to any order in the coupling strength. Algebraic computer programs are supplied on accompanying World Wide Web pages.
Kleinert earned his doctorate in at the University of Colorado, Boulder. This so-called variational perturbation theory yields at present the most accurate theory of critical exponents  observable close to second-order phase transitions , as confirmed for superfluid helium in satellite experiments. Landau for phase transitions which Kleinert developed in the books on Gauge Fields in Condensed Matter. 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. At the summer school in Erice he proposed the existence of broken supersymmetry in atomic nuclei,  which has since been observed experimentally.