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Foundations of Physics

, Volume 44, Issue 5, pp 546–556 | Cite as

Quantum Field Theory of Black-Swan Events

  • H. KleinertEmail author
Article

Abstract

Free and weakly interacting particles are described by a second-quantized nonlinear Schrödinger equation, or relativistic versions of it. They describe Gaussian random walks with collisions. By contrast, the fields of strongly interacting particles are governed by effective actions, whose extremum yields fractional field equations. Their particle orbits perform universal Lévy walks with heavy tails, in which rare events are much more frequent than in Gaussian random walks. Such rare events are observed in exceptionally strong windgusts, monster or rogue waves, earthquakes, and financial crashes. While earthquakes may destroy entire cities, the latter have the potential of devastating entire economies.

Keywords

Quantum field theory Improbable events Financial crahes Monster waves 

Notes

Acknowledgements

I am grateful to P. Jizba, N. Laskin, M. Lewenstein, A. Pelster, and M. Zwierlein for useful comments, and to Fabio Scardigli, Luca Di Fiore, and Matteo Nespoli for their hospitality in Taipeh during their Workshop Horizons of Quantum Physics (http://www.quantumhorizons.org).

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikFreie Universität BerlinBerlinGermany

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