Hagen Kleinert (born 15 June 1941) is professor of

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

at the

Free University of Berlin The Free University of Berlin (, often abbreviated as FU Berlin or simply FU) is a public research university in Berlin, Germany. It is consistently ranked among Germany's best universities, with particular strengths in political science and t ...

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwee ...

(since 1968)
Honorary Doctor
at the

West University of Timișoara The West University of Timișoara ( ro, Universitatea de Vest din Timișoara; abbreviated UVT) is a public higher education institution located in Timișoara. Classified by the Ministry of National Education as a university of education and s ...

and
at th

in

Bishkek Bishkek ( ky, Бишкек), ), formerly Pishpek and Frunze, is the capital and largest city of Kyrgyzstan. Bishkek is also the administrative centre of the Chüy Region. The region surrounds the city, although the city itself is not part of ...

. He is als
Honorary Member
of th

For his contributions to particle and solid state physics he wa

the

Max Born Prize The Max Born Medal and Prize is a scientific prize awarded yearly by the German Physical Society (DPG) and the British Institute of Physics (IOP) in memory of the German physicist Max Born, who was a German-Jewish physicist, instrumental in the ...

2008 wit
Medal
His contribution to th
memorial volume
celebrating the 100th birthday of Lev Davidovich Landau earned him the Majorana Prize 2008 with Medal. He is married to Dr. Annemarie Kleinert since 1974 with whom he has a so
Michael Kleinert

Publications

Kleinert has written ~420 papers on

mathematical physics Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developm ...

and the

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...

elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions ( quarks, leptons, ...

s, nuclei, solid state systems,

liquid crystal Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid crystal may flow like a liquid, but its molecules may be oriented in a crystal-like way. Th ...

biomembrane A biological membrane, biomembrane or cell membrane is a selectively permeable membrane that separates the interior of a cell from the external environment or creates intracellular compartments by serving as a boundary between one part of the ...

s, microemulsions,

polymer A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...

s, and the theory of

financial markets A financial market is a market in which people trade financial securities and derivatives at low transaction costs. Some of the securities include stocks and bonds, raw materials and precious metals, which are known in the financial ma ...

. He has written several books on theoretical physics, the most notable of which, ''Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets,'' has been published in five editions since 1990 and has received enthusiastic reviews.

Education

He studied physics at the

Leibniz University Hannover Gottfried Wilhelm Leibniz University Hannover (german: Gottfried Wilhelm Leibniz Universität), also known as the University of Hannover, is a public research university located in Hanover, Germany. Founded on 2 May 1831 as Higher Vocational Sc ...

between 1960 and 1963, and at several American universities including

Georgia Institute of Technology The Georgia Institute of Technology, commonly referred to as Georgia Tech or, in the state of Georgia, as Tech or The Institute, is a public research university and institute of technology in Atlanta, Georgia. Established in 1885, it is part ...

, where he learned

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

as a graduate student from

George Gamow George Gamow (March 4, 1904 – August 19, 1968), born Georgiy Antonovich Gamov ( uk, Георгій Антонович Гамов, russian: Георгий Антонович Гамов), was a Russian-born Soviet and American polymath, theoret ...

, one of the fathers of the

Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...

theory. Kleinert earned his doctorate in 1967 at the

University of Colorado, Boulder The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a public research university in Boulder, Colorado. Founded in 1876, five months before Colorado became a state, it is the flagship university of the University of Colorado s ...

Career

As a young professor in 1972, Kleinert visited

Caltech The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

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 In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n = a_0 + a_1 (x - c) + a_2 (x - c)^2 + \dots where ''an'' represents the coefficient of the ''n''th term and ''c'' is a con ...

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 transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states ...

s, 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 Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...

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 Singular may refer to: * Singular, the grammatical number that denotes a unit quantity, as opposed to the plural and other forms * Singular homology * SINGULAR, an open source Computer Algebra System (CAS) * Singular or sounder, a group of boar ...

potentials using path integrals. Within the quantum field theories of quarks he found the origin of th
algebra of Regge residues
conjectured by N. Cabibbo, L. Horwitz, and Y. Ne'eman (se
p. 232
in reference).

Discoveries

For superconductors he predicted in 1982 a tricritical point in the

phase diagram A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases (such as solid, liquid or gaseous ...

between type-I and type-II superconductors where the order of the transition changes from second to first. The predictions were confirmed in 2002 by

Monte Carlo Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is ...

computer simulation Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be deter ...

s. The theory is based on a disorder field theory dual to the order field theory of L.D. Landau for

s which Kleinert developed in the books on ''Gauge Fields in Condensed Matter''. In this theory, the statistical properties of fluctuating

vortex In fluid dynamics, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in ...

or defect lines are described as elementary excitations with the help of fields, whose

Feynman diagram In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduc ...

s are the pictures of the lines. At the 1978 summer school in

Erice Erice (; scn, Èrici) is a historic town and '' comune'' in the province of Trapani, Sicily, in southern Italy. Geography The main town of Erice is located on top of Mount Erice, at around above sea level, overlooking the city of Trapani ...

he proposed the existence of broken

supersymmetry In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...

in atomic nuclei, which has since been observed experimentally. His theory of collective quantum fields and the Hadronization of Quark Theories are prototypes for numerous developments in the theory of condensed matter,

nuclear Nuclear may refer to: Physics Relating to the nucleus of the atom: *Nuclear engineering *Nuclear physics *Nuclear power *Nuclear reactor *Nuclear weapon *Nuclear medicine *Radiation therapy *Nuclear warfare Mathematics *Nuclear space *Nuclear ...

and elementary particle physics. Together with K. Maki he proposed and clarified in 1981 a possible

icosahedral phase A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical ...

of quasicrystals. This structure was discovered three years later in aluminum transition metal alloys by Dan Shechtman, which earned him the Nobel Prize 2011. In 2006, he considered the existence of a novel Riemann particle. The experimental verification is still missing. Se
historical notes

String theory contributions

In 1986 he introduced stiffness into the theory of strings, which had formerly been characterized by tension alone. This greatly improved the description of the physical properties of strings. The Russian physicist A. Polyakov simultaneously proposed a similar extension, and so the model is now known as th
Polyakov-Kleinert string
.

Theory of distributions

Together with A. Chervyakov, Kleinert developed an extension of the theory of distributions from linear spaces to

semigroup In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multiplicatively: ''x''·''y'', or simply ''xy'', ...

s by defining their products uniquely (in the mathematical theory, only linear combinations are defined). The extension is motivated by the physical requirement that the corresponding path integrals must be invariant under coordinate transformations, which is necessary for the equivalence of the

path integral formulation The path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional i ...

to Schrödinger theory.

String theory alternative

As an alternative to

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...

, Kleinert 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 o
Planck-Kleinert crystal
In this model, matter creates defects in spacetime which generate curvature. This curvature reproduces all the effects of

, but leads to different physics than string theory at the scale of the Planck length. This theory inspired Italian artis
Laura Pesce
to create glass sculptures entitle

(see also lower left o

.

Current work

Kleinert is a senior member of the faculty for the International Relativistic Astrophysics Ph

Project, which forms part of the international network for astrophysics (

ICRANet ICRANet, the International Center for Relativistic Astrophysics Network, is an international organization which promotes research activities in relativistic astrophysics and related areas. Its members are four countries and three Universities an ...

). He was also involved in the

European Science Foundation The European Science Foundation (ESF) is an association of 11 member organizations devoted to scientific research in 8 European countries. ESF is an independent, non-governmental, non-profit organisation that promotes the highest quality science ...

's projec
Cosmology in the Laboratory
Kleinert's 60th birthday was honored by a

Festschrift In academia, a ''Festschrift'' (; plural, ''Festschriften'' ) is a book honoring a respected person, especially an academic, and presented during their lifetime. It generally takes the form of an edited volume, containing contributions from the ...

and
Festcolloquium
with 65 contributions by international colleagues (for instance Y. Ne'eman, R. Jackiw, H. Fritzsch, R. Ruffini, C. DeWitt, L. Kauffman, J. Devreese, and K. Maki).

Books

* ''Gauge Fields in Condensed Matter'', Vol. I, " SUPERFLOW AND VORTEX LINES", pp. 1–742, Vol. II, "STRESSES AND DEFECTS", pp. 743–1456,
World Scientific (Singapore, 1989)
Paperback '' (also available online

an

'' * ''Critical Properties of φ⁴-Theories''

Paperback '' (also availabl
online
(together with V. Schulte-Frohlinde)'' * ''Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets'', 5th edition

(also availabl
online
* ''Multivalued Fields in Condensed Matter, Electrodynamics, and Gravitation'',

(also availabl
online
* ''Proceedings of th
Eleventh Marcel Grossmann Meeting
on

General Relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

'',
World Scientific (Singapore, 2008)
(together with R.T. Jantzen) * ''Particles and Quantum Fields'',
World Scientific (Singapore, 2016)
(also availabl
online

References

External links

Personal homepage
{{DEFAULTSORT:Kleinert, Hagen 1941 births Living people People from Twardogóra People from the Province of Lower Silesia 20th-century German physicists University of Hanover alumni Georgia Tech alumni Free University of Berlin faculty 21st-century German physicists