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

H.a Tolhoek

Physica A: Statistical Mechanics and its Applications, 1977, vol. 86, issue 2, 278-302

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.

Date: 1977
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:86:y:1977:i:2:p:278-302

DOI: 10.1016/0378-4371(77)90032-2

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