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The mathematical theory of quantum fields

Modern Analysis And New Physical Theories

Part of the Lecture Notes in Mathematics book series (LNM,volume 140)

Keywords

  • Unitary Representation
  • Unitary Group
  • Free Field
  • Complex Hilbert Space
  • Weyl Algebra

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References

The indicated results were largely developed in theses at M.I.T. or the University of Chicago, and/or published in articles referred to in the following surveys which I have made

  1. Mathematical problems of relativistic physics. Providence (Amer. Math. Soc.), 1963.

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  2. Local non-linear functions of quantum fields. To appear in Proceedings of the Conference in Honor of Marshall H. Stone (Chicago, May, 1968), forthcoming (Springer).

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See in particular for some quoted results

  1. M. Weinless, Vacuums of linear quantum fields. To appear in Journal of Functional Analysis.

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The basic relevant technical work on non-linear quantum fields includes the following of my papers

  1. Notes towards the construction of non-linear relativistic quantum fields. I. Proc. Nat. Acad. Sci. 57 (1967), 1178–1183.

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  2. Non-linear functions of weak processes. To appear in Jour. Funct. Anal.

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One of clearest introductions to theoretical physical practice concerning perturbative renormalization theory is

  1. F. Mandl, Introduction to quantum field theory. New York (Interscience), 1959.

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© 1970 Springer-Verlag

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Segal, I.E. (1970). The mathematical theory of quantum fields. In: Taam, C.T. (eds) Lectures in modern analysis and applications II. Lecture Notes in Mathematics, vol 140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100065

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  • DOI: https://doi.org/10.1007/BFb0100065

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