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Analytic Properties of Wightman Functions in Coordinate Space

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General Principles of Quantum Field Theory

Part of the book series: Mathematical Physics and Applied Mathematics ((MPAM,volume 10))

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Abstract

We saw (Theorem 8.5) that by virtue of the spectrum condition, the Wightman functions w(xl,…, x n ) = W1,…,ξn−1) are boundary values of functions W1,…,ζn−1) of ζ1,…, ζn−1 that are holomorphic in the past tubes T n−1 (8.41). It turns out that the combination of the spectrum property and Lorentz-invariance provides extra information about analyticity, in particular, it allows one to continue the functions analytically to a wider domain (called the extended tube). This theorem, due to Bargmann, Hall and Wightman, lies at the basis of the TCP theorem and the theorem on the connection between spin and statistics, which we shall become acquainted with in this chapter.

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© 1990 Kluwer Academic Publishers

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Bogolubov, N.N., Logunov, A.A., Oksak, A.I., Todorov, I.T., Gould, G.G. (1990). Analytic Properties of Wightman Functions in Coordinate Space. In: Bogolubov, N.N., Logunov, A.A., Oksak, A.I., Todorov, I.T. (eds) General Principles of Quantum Field Theory. Mathematical Physics and Applied Mathematics, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0491-0_9

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  • DOI: https://doi.org/10.1007/978-94-009-0491-0_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6707-2

  • Online ISBN: 978-94-009-0491-0

  • eBook Packages: Springer Book Archive

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