Career
As a young professor in 1972, Kleinert visited Caltech and was impressed by noted US physicist Richard Feynman. Later, Kleinert was to collaborate with Feynman in some of the latter's last work. This collaboration 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 observable close to second-order phase transitions, as confirmed for superfluid helium in satellite experiments. He also discovered an alternative to Feynman's time-sliced path integral construction which can be used to solve the path integral formulations of the hydrogen atom and the centrifugal barrier, i.e. to calculate their energy levels and eigenstates, as special cases of a general strategy for treating systems with singular potentials using path integrals.
Within the quantum field theories of quarks he found the origin of the algebra of Regge residues conjectured by N. Cabibbo, L. Horwitz, and Y. Ne'eman (see p.232 in Ref.).
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