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Integration of the Tomonaga-Schwinger equation

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Abstract

Some integrations of the Tomonaga-Schwinger equation with a non-local interaction are studied with mathematical rigor. It is proved that the related initial value problem has a unique solution in any finite region of the space-time corresponding to each set of space-like surfaces which covers the region. Such an analysis can be extended to the case of quantum electrodynamics by the aid of a Lorentz-invariant topology introduced in the *-algebra of electromagnetic field operators.

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References

  1. Yosida, K.: Functional Analysis. Berlin-Heidelberg-New York: Springer 1965

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  2. Kato, T.: J. Math. Soc. Japan5, 208–234 (1953); Comm. Pure Appl. Math.9, 479–486 (1956)

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Engineering, Gifu University, Kagamihara, Japan

    Hitoshi Wakita

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  1. Hitoshi Wakita
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Communicated by H. Araki

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Wakita, H. Integration of the Tomonaga-Schwinger equation. Commun.Math. Phys. 50, 61–68 (1976). https://doi.org/10.1007/BF01608555

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  • DOI: https://doi.org/10.1007/BF01608555

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