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Higher order field equations II; Limit properties of green's functions

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  • Tolhoek, H.A

Abstract

In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions GMR(x) and GMA(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for |M| → ∞ the Green's functions GMR(x) and GMA(x) approach the Green's functions ΔR(x) and ΔA(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of GMA(x) and GMA(x) is the same as of ΔR(x) and ΔA(x) - and also the same as for DR(x) and DA(x) for t→ ± ∞, where DR and DA are the Green n's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense.

Suggested Citation

  • Tolhoek, H.A, 1977. "Higher order field equations II; Limit properties of green's functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 86(2), pages 278-302.
    • Handle: RePEc:eee:phsmap:v:86:y:1977:i:2:p:278-302
    DOI: 10.1016/0378-4371(77)90032-2
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    References listed on IDEAS

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    1. Mattos, Antônio Carlos Marques, 1972. "Informática: o sistema de palavras-chave do contexto (K.W.I.C.)," RAE - Revista de Administração de Empresas, FGV-EAESP Escola de Administração de Empresas de São Paulo (Brazil), vol. 12(4), October.
    2. Meuwese, A.J. & Jansen, H.J.F. & Tolhoek, H.A., 1976. "Wave propagation according to higher order field equations I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 82(1), pages 72-96.
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    1. Meuwese, A.J. & Jansen, H.J.F. & Tolhoek, H.A., 1976. "Wave propagation according to higher order field equations I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 82(1), pages 72-96.

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