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Some Jump Processes in Quantum Field Theory

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Interacting Stochastic Systems

Summary

A jump process for the positions of interacting quantum particles on a lattice, with time-dependent transition rates governed by the state vector, was first considered by J.S. Bell. We review this process and its continuum variants involving “minimal” jump rates, describing particles as they get created, move, and get annihilated. In particular, we sketch a recent proof of global existence of Bell’s process. As an outlook, we suggest how methods of this proof could be applied to similar global existence questions, and underline the particular usefulness of minimal jump rates on manifolds with boundaries.

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Author information

Authors and Affiliations

  1. Dipartimento di Fisica and INFN sezione di Genova, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy

    Roderich Tumulka

  2. Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstr. 39, 80333, München, Germany

    Hans-Otto Georgii

Authors
  1. Roderich Tumulka
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  2. Hans-Otto Georgii
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Editor information

Editors and Affiliations

  1. Fakultät II, Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Jean-Dominique Deuschel

  2. Fachbereich Mathematik und Physik Mathematisches Institut, Universität Erlangen, Bismarckstr. 1 1/2, 91054, Erlangen, Germany

    Andreas Greven

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Tumulka, R., Georgii, HO. (2005). Some Jump Processes in Quantum Field Theory. In: Deuschel, JD., Greven, A. (eds) Interacting Stochastic Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27110-4_4

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