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Title of Journal: Nuovo Cimento A 19651970

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Abbravation: Il Nuovo Cimento A (1965-1970)

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Springer Berlin Heidelberg

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DOI

10.1007/bf01815071

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1826-9869

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Existence of solutions of partialwave dispersion

Authors: A P Contogouris A Martin
Publish Date: 2016/01/11
Volume: 49, Issue: 1, Pages: 61-72
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Abstract

It is shown that for lefthand discontinuities which asymptotically exceed certain limits imposed by unitarity the partialwave dispersion relation admits no ghostfree solutions However for discontinuities which on the left tend to a limit λ 0λ1 the singular integral equation that arises by application of the usualN/D approach is shown to lead to a oneparameter manifold of ghostfree solutions in particular a specific solution which is analytic at λ=0 belongs to this manifold The variation of the zeros of theD function for varying λ is shown explicitly in a simple exampleПоказано что для левосторонних разрывов которые асимптотически превосходят определенные пределы накладываемые унитарностью дисперсионное соотношение для парциальной волны не допускает нефизические «духовые» свободные решения Однако для разрывов которые слева стремятся к пределе л 0λ1 показано что сингулярное интегральное уравнение которое получает при исполязовании обычногоN/D приближения ведет к однопараметрическому множеству нефизических «духовых» свободных решений в частности частное решение которое аналитично при λ=0 принадлезит л этому множеству Точно показано изменение нулеиD функции для различных λ на простом примереSi dimostra che per discontinuità a sinistra che superino asintoticamente certi limiti impositi dall’unitarietà le relazioni di dispersione in onde parziali non ammettono alcuna soluziono priva di fantasmi Tuttavia per discontinuità che a sinistra tendono al limite λ 0λ1 si dimostra che l’equazione integrale singolare che nasce dall’applicazione dell’usuale metodoN/D porta ad una molteplicità ad un parametro di soluzioni prive di fantasmi in particolare appartiene a questa molteplicità una specifica soluzione analitica per λ=0 Si mostra esplicitamente in un semplice esempio la variazione degli zeri della funzioneD per λ variabile

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