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Path Integrals in Quantum Mechanics, Statistics,. Polymer Physics, and Financial Markets. Hagen Kleinert. Professor of Physics. Freie Universität Berlin.

**Table of contents**

- My Shopping Bag
- 2008 Born medal and prize
- Path Integrals
- PATH INTEGRALS IN QUANTUM MECHANICS, STATISTICS, POLYMER PHYSICS AND FINANCIAL MARKETS

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.

### My Shopping Bag

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.

Hagen Kleinert.

Request Inspection Copy. Hagen Kleinert. This is the fourth, expanded edition of the comprehensive textbook published in 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.

## 2008 Born medal and prize

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.

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## Path Integrals

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## PATH INTEGRALS IN QUANTUM MECHANICS, STATISTICS, POLYMER PHYSICS AND FINANCIAL MARKETS

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