This is the fifth, 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 quantummechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's timesliced formula to include singular attractive 1/r and 1/r2potentials. The second is a new nonholonomic mapping principle carrying physical laws in flat spacetime to spacetimes with curvature and torsion, which leads to timesliced path integrals that are manifestly invariant under coordinate transformations. In addition to the timesliced definition, the author gives a perturbative, coordinateindependent 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 products of distributions. The powerful FeynmanKleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent results. The convergence is uniform from weak to strong couplings, opening a way to precise evaluations of analytically unsolvable path integrals in the strongcoupling regime where they describe critical phenomena. Tunneling processes are treated in detail, with applications to the lifetimes of supercurrents, the stability of metastable thermodynamic phases, and the largeorder behavior of perturbation expansions. A variational treatment extends the range of validity to small barriers. A corresponding extension of the largeorder perturbation theory now also applies to small orders. Special attention is devoted to path integrals with topological restrictions needed to understand the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The ChernSimons 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 BlackScholes formula for option prices are developed which account for the fact, recently experienced in the world markets, that large fluctuations occur much more frequently than in Gaussian distributions.
About Hagen Kleinert
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Author  :  Hagen Kleinert 
Publisher  :  World Scientific Publishing Co Pte Ltd 
Data Published  :  30 May 2020 
ISBN  :  9814273562 
EAN  :  9789814273565 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  1579 pages 
Age +  :  18 years 
Language  :  English 
Rating  : 
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