Background
Kleinert, Hagen Michael was born on June 15, 1941 in Festenberg, Silesia, Germany. Son of Walter and Hedwig (Ruby) Kleinert.
(This is the fourth, expanded edition of the comprehensive...)
This is the fourth, expanded edition of the comprehensive textbook published in 1990 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 first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. 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. The author's other book on 'Critical Properties of Theories' gives a thorough introduction to the field of critical phenomena and develops new powerful resummation techniques for the extraction of physical results from the divergent perturbation expansions.
https://www.amazon.com/Integrals-Quantum-Mechanics-Statistics-Financial/dp/9814273562?SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook-20&linkCode=sp1&camp=2025&creative=165953&creativeASIN=9814273562
(Path Integrals in Quantum Mechanics, Statistics, Polymer ...)
Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets PaperbackHagen Kleinert (Author)
https://www.amazon.com/Integrals-Mechanics-Statistics-Financial-Kleinert/dp/B003TKXL4U?SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook-20&linkCode=sp1&camp=2025&creative=165953&creativeASIN=B003TKXL4U
(This book is the first to develop a unified gauge theory ...)
This book is the first to develop a unified gauge theory of condensed matter systems dominated by vortices or defects and their long-range interactions. Gauge fields provide the only means of describing these interactions in terms of local fields, rendering them accessible to standard field theoretic techniques. Two particularly important examples, superfluid systems and crystals, are treated in great detail. The theory is developed in close contact with physical phenomena and evolves naturally from conventional descriptions of the systems. In addition to gauge fields, the book introduces the important new concept of disorder fields for ensembles of line-like defects. The combined field theory allows for a new understanding of the important phase transitions superfluid ‘normal and solid’ liquid. Apart from the above, the book presents the general differential geometry of defects in spaces with curvature and torsion and establishes contact with the modern theory of gravity with torsion. This book is written for condensed matter physicists and field theorists. It can be used as a textbook for a second-year graduate course or as supplementary reading for courses in the areas of condensed matter and solid state physics, statistical mechanics, and field theory.
https://www.amazon.com/Gauge-Fields-Condensed-Matter-Superflow/dp/9971502119?SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook-20&linkCode=sp1&camp=2025&creative=165953&creativeASIN=9971502119
(This is the third, significantly expanded edition of the ...)
This is the third, significantly expanded edition of the comprehensive textbook published in 1990 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 first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. 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 entaglement 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. The author's other book on 'Critical Properties of phi4 Theories' gives a thorough introduction to the field of critical phenomena and develops new powerful resummation techniques for the extraction of physical results from the divergent perturbation expansions.
https://www.amazon.com/Integrals-Quantum-Mechanics-Statistics-Financial/dp/9812381074?SubscriptionId=AKIAJRRWTH346WSPOAFQ&tag=prabook-20&linkCode=sp1&camp=2025&creative=165953&creativeASIN=9812381074
Kleinert, Hagen Michael was born on June 15, 1941 in Festenberg, Silesia, Germany. Son of Walter and Hedwig (Ruby) Kleinert.
Bachelor of Science, Hannover University Veterinary School, Germany, 1962. Master of Science, Georgia Institute of Technology, 1964. Doctor of Philosophy, Colorado University, 1967.
Habilitation, Free University, Berlin, 1969.
Assistant professor, Montana State University, Bozeman, 1967-1968; associate professor physics, Free U., Berlin, 1968-1975; professor physics, Free U., Berlin, since 1975. Visiting professor California Institute Technology, 1972.
(This textbook on the theory and applications of path inte...)
(This book is the first to develop a unified gauge theory ...)
(This is the third, significantly expanded edition of the ...)
(This is the fourth, expanded edition of the comprehensive...)
(Path Integrals in Quantum Mechanics, Statistics, Polymer ...)
Married Annemarie E. Ludwig, May 30, 1974. 1 child, Michael.