Hagen Kleinert
Encyclopedia
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
at the Free University of Berlin
Free University of Berlin
Freie Universität Berlin is one of the leading and most prestigious research universities in Germany and continental Europe. It distinguishes itself through its modern and international character. It is the largest of the four universities in Berlin. Research at the university is focused on the...
, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
(since 1968),
Honorary Doctor at the
West University
West University of Timisoara
The West University of Timişoara is a university located in Timişoara, Romania. Established in 1962, it is organized in 11 Faculties.-Organization:...
of Timişoara
Timisoara
Timișoara is the capital city of Timiș County, in western Romania. One of the largest Romanian cities, with an estimated population of 311,586 inhabitants , and considered the informal capital city of the historical region of Banat, Timișoara is the main social, economic and cultural center in the...
, and
at the
Kyrgyz-Russian Slavic University
in Bishkek
Bishkek
Bishkek , formerly Pishpek and Frunze, is the capital and the largest city of Kyrgyzstan.Bishkek is also the administrative centre of Chuy Province which surrounds the city, even though the city itself is not part of the province but rather a province-level unit of Kyrgyzstan.The name is thought to...
. He is also
Honorary Member of the
Russian Academy of Creative Endeavors. For his contributions to particle and solid state physics he was awarded the Max Born prize
Max Born prize
The Max Born Prize is a scientific prize awarded yearly by the German Physical Society and the British Institute of Physics in memory of the German physicist Max Born. The terms of the award are that it is "to be presented for outstanding contributions to physics"...
2008 with Medal.
His contribution to the memorial volume celebrating the 100th birthday of Lev Davidovich Landau earned him the Majorana Prize
Majorana Prize
The Majorana Prize is awarded annually by the Electronic Journal of Theoretical Physics for outstanding contributions to theoretical physics. It is named after Ettore Majorana, an Italian theoretical physicist who began promising work on neutrino masses and Majorana equation...
2008 with Medal.
Publications
Kleinert has written more than 370 papers on mathematical physicsMathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
and the physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
of elementary particle
Elementary particle
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s, nuclei
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
, solid state
Solid
Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...
systems, liquid crystal
Liquid crystal
Liquid crystals are a state of matter that have properties between those of a conventional liquid and those of a solid crystal. For instance, an LC may flow like a liquid, but its molecules may be oriented in a crystal-like way. There are many different types of LC phases, which can be...
s, biomembranes, microemulsion
Microemulsion
Microemulsions are clear, thermodynamically stable, isotropic liquid mixtures of oil, water and surfactant, frequently in combination with a cosurfactant. The aqueous phase may contain salt and/or other ingredients, and the "oil" may actually be a complex mixture of different hydrocarbons and olefins...
s, polymer
Polymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...
s, and the theory of financial markets. 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
After his first years as a student at the University of Hanover and Georgia Institute of TechnologyGeorgia Institute of Technology
The Georgia Institute of Technology is a public research university in Atlanta, Georgia, in the United States...
, he learned general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
as a graduate student from George Gamov, one of the fathers of the Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
theory.
Career
As a young professor in 1972, Kleinert visited CaltechCalifornia Institute of Technology
The California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
and was impressed by noted US physicist Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
. 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 transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
s, as confirmed for superfluid
Superfluid
Superfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...
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
Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...
formulations of the hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
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
Mathematical singularity
In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability...
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
Nicola Cabibbo
Nicola Cabibbo was an Italian physicist, best known for his work on the weak interaction. He was also the president of the Italian National Institute of Nuclear Physics from 1983 to 1992, and from 1993 until his death he was the president of the Pontifical Academy of Sciences...
, L. Horwitz, and
Y. Ne'eman
Yuval Ne'eman
Yuval Ne'eman , was a renowned Israeli theoretical physicist, military scientist, and politician. He was a minister in the Israeli government in the 1980s and early 1990s.-Biography:...
(see p.232 in Ref.).
Together with K. Maki he clarified the structure of the icosahedral phase of quasicrystal
Quasicrystal
A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry...
s. See historical notes.
Discoveries
For superconductors he predicted in 1982 a tricritical point in the phase diagramPhase diagram
A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium...
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 method
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used in computer simulations of physical and mathematical systems...
computer simulations
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...
.
The theory is based on a disorder field theory dual
Duality (mathematics)
In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often by means of an involution operation: if the dual of A is B, then the dual of B is A. As involutions sometimes have...
to the order field theory of L.D. Landau
Lev Landau
Lev Davidovich Landau was a prominent Soviet physicist who made fundamental contributions to many areas of theoretical physics...
for phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
s which Kleinert developed in the books on Gauge Fields in Condensed Matter. In this theory, the statistical properties of fluctuating vortex
Vortex
A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...
or defect lines
Crystallographic defect
Crystalline solids exhibit a periodic crystal structure. The positions of atoms or molecules occur on repeating fixed distances, determined by the unit cell parameters. However, the arrangement of atom or molecules in most crystalline materials is not perfect...
are described as elementary excitations with the help of fields, whose Feynman diagram
Feynman diagram
Feynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...
s are the pictures of the lines.
At the 1978 summer school in Erice
Erice
Erice is a historic town and comune in the province of Trapani in Sicily, Italy.Erice is located on top of Mount Erice, at around 750m above sea level, overlooking the city of Trapani, the low western coast towards Marsala, the dramatic Punta del Saraceno and Capo san Vito to the north-east, and...
he proposed the existence of broken supersymmetry
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
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
Condensed Matter
Condensed matter may refer to several things*Condensed matter physics, the study of the physical properties of condensed phases of matter*European Physical Journal B: Condensed Matter and Complex Systems, a scientific journal published by EDP sciences...
, nuclear
Nuclear physics
Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...
and elementary particle physics.
String theory contributions
In 1986 he introduced stiffness into the theory of stringsString theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
,
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 the Polyakov-Kleinert string.
Theory of distributions
Together with A. Chervyakov, Kleinert developed an extension of the theory of distributionsDistribution (mathematics)
In mathematical analysis, distributions are objects that generalize functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative...
from linear spaces to semigroup
Semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that there might not exist an identity element...
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
Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...
must be invariant under coordinate transformations, which is necessary for the equivalence of the path integral formulation
Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...
to Schrödinger theory
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....
.
String theory alternative
As an alternative to string theoryString theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
, Kleinert used the complete analogy between non-Euclidean geometry
Non-Euclidean geometry
Non-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
and the geometry of crystals with defects
Crystallographic defect
Crystalline solids exhibit a periodic crystal structure. The positions of atoms or molecules occur on repeating fixed distances, determined by the unit cell parameters. However, the arrangement of atom or molecules in most crystalline materials is not perfect...
to construct a model of the universe called the World Crystal
World Crystal
Theoretical models of the universe are valid only at large distances. The properties of spacetime at ultrashort distances of the order of the Planck length are completely unknown since they have not been explored by any experiment...
or Planck-Kleinert crystal. In this model, matter creates defects in spacetime which generate curvature. This curvature reproduces all the effects of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, but 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 entitled "world crystal" (see also lower left on this page).
Current
Kleinert is a senior member of the faculty for the International Relativistic Astrophysics Ph.D. (IRAP) Project, which forms part of the international network for astrophysics (ICRANetICRANet
ICRANet, the International Center for Relativistic Astrophysics, is an international organization promoting research activities with members in four countries at three Universities and Research Centres...
). He was also involved in the European Science Foundation
European Science Foundation
The European Science Foundation is an association of 78 member organisations devoted to scientific research in 30 European countries. It is an independent, non-governmental, non-profit organisation that facilitates cooperation and collaboration in European research and development, European...
's project Cosmology in the Laboratory.
Kleinert's 60. birthday was honored by a Festschrift
Festschrift
In academia, a Festschrift , is a book honoring a respected person, especially an academic, and presented during his or her lifetime. The term, borrowed from German, could be translated as celebration publication or celebratory writing...
and a Festcolloquium with 65 contributions by international colleagues (for instance Y. Ne'eman
Yuval Ne'eman
Yuval Ne'eman , was a renowned Israeli theoretical physicist, military scientist, and politician. He was a minister in the Israeli government in the 1980s and early 1990s.-Biography:...
, R. Jackiw
Roman Jackiw
Roman W. Jackiw is a theoretical physicist and Dirac Medallist. Born in Poland, Jackiw received his PhD from Cornell University in 1966 under Hans Bethe and Kenneth Wilson...
, H. Fritzsch, R. Ruffini
Remo Ruffini
Remo Ruffini is Professor of Theoretical Physics at the University of Rome "Sapienza", since 1978...
, C. DeWitt, L. Kauffman, J. Devreese
Jozef T. Devreese
Jozef T. Devreese is a Belgian scientist, with a long career in condensed matter physics. He is Professor Emeritus of Theoretical Physics at the Universiteit Antwerpen.He obtained a Ph.D...
, 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 ISBN 9971-5-0210-0 (also available online: Vol. I and Vol. II)
- Critical Properties of φ4-Theories, World Scientific (Singapore, 2001); Paperback ISBN 981-02-4658-7 (also available online) (together with V. Schulte-Frohlinde)
- Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 5th edition, World Scientific (Singapore, 2009) (also available online)
- Multivalued Fields in in Condensed Matter, Electrodynamics, and Gravitation, World Scientific (Singapore, 2008) (also available online)
- Proceedings of the Eleventh Marcel Grossmann Meeting on General RelativityGeneral relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, World Scientific (Singapore, 2008) (together with R.T. Jantzen)