White Noise pp 399-434 | Cite as

Applications to Quantum Field Theory

  • Takeyuki Hida
  • Hui-Hsiung Kuo
  • Jürgen Potthoff
  • Ludwig Streit
Part of the Mathematics and Its Applications book series (MAIA, volume 253)


In this chapter we shall discuss various aspects of quantum field theory which can be formulated in the framework developed in Chapters 1 to 5. We begin with this section containing an introduction to quantum field theory, which is intended to give the reader an idea about the basic questions and notions in this area. Here we make a number of heuristic and informal considerations, referring to the pertaining literature for mathematically more rigorous treatments (when available). For a general background on quantum field theory which is more oriented towards physics we refer to the books of Bjørken and Drell (1965), Bogoliubov and Shirkov (1959), Itzykson and Zuber (1980), Schweber (1961). Mathematically rigorous treatments of the foundations of quantum field theory are given in the monographs by Bogoliubov et al. (1975), Jost (1965) and Streater and Wightman (1964). Modern aspects of mathematical quantum field theory, in particular Euclidean quantum field theory, are treated in the books by Simon (1974), and Glimm and Jaffe (1981).


Quantum Field Theory Dirichlet Form Free Field Canonical Commutation Relation Euclidean Measure 
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Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Takeyuki Hida
    • 1
  • Hui-Hsiung Kuo
    • 2
  • Jürgen Potthoff
    • 3
  • Ludwig Streit
    • 4
    • 5
  1. 1.Department of MathematicsMeijo UniversityNagoyaJapan
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA
  3. 3.Universität MannheimMannheimGermany
  4. 4.BiBos, Universität BielefeldBielefeldGermany
  5. 5.Universidade da MadeiraFunchal, MadeiraPortugal

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