Analytic and Probabilistic Aspects of Lévy Processes and Fields in Quantum Theory

  • Sergio Albeverio
  • Barbara Rüdiger
  • Jiang-Lun Wu

Abstract

A review of work on the description of generators and processes associated with stochastic (partial or pseudo-) differential equations driven by general white noises (including jump as well as diffusion parts) is given. Processes with finite- or infinite-dimensional state space are described in a unified way using the theory of Dirichlet forms, combined with the technique of subordination of processes. In particular the analytic problems arising from subordinating sub-Markov semigroups are described. As examples the subordination of stochastic quantization processes is presented. It is also described how stochastic partial differential or pseudodifferential equations are used to construct relativistic quantum fields in indefinite metric with nontrivial scattering in four space- time dimensions.

Keywords

Filtration Manifold Covariance Assure Convolution 

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Sergio Albeverio
    • 1
    • 2
    • 3
    • 4
    • 5
  • Barbara Rüdiger
    • 1
  • Jiang-Lun Wu
    • 1
    • 6
    • 7
  1. 1.Institut für Angewandte Mathematik, SFB 256Universität BonnBonnGermany
  2. 2.SFB 237Essen-Bochum-DüsseldorfGermany
  3. 3.BiBoS-Research CentreBielefeldGermany
  4. 4.CERFIMLocarnoSwitzerland
  5. 5.Acc. Arch.USISwitzerland
  6. 6.Department of MathematicsUniversity of Wales SwanseaSwanseaUK
  7. 7.Institute of Applied MathematicsAcademia SinicaBeijingPeople’s Republic of China

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