Summary
The scattering of light by light is considered with the aid of double dispersion relations. The spectral functions are easily obtained, in the lowest perturbative order, by means of the Cutkosky rules and a Mandelstam representation is explicitly written. This approach is very suitable for the symmetry properties of this scattering reaction and allows to obtain the differential cross-section in a straightforward way for all the values of the energy and of the angle. In order to give a detailed exposition of the method we consider in this paper only that amplitude which describes the scattering of linearly polarized photons in a direction perpendicular to the scattering plane.
Riassunto
Si considera l’urto fotone-fotone facendo uso delle relazioni di dispersione doppie. Le funzioni spettrali si calcolano facilmente, nell’approssimazione perturbativa di ordine più basso, applicando le regole di Cutkosky e si può così scrivere esplicitamente una rappresentazione di Mandelstam. Questa impostazione è particolarmente adatta alle proprietà di simmetria del problema d’urto considerato e permette di ottenere, con estrema facilità, la sezione d’urto differenziale per qualsiasi valore dell’energia e dell’angolo. Per illustrare il metodo in dettaglio, in questo lavoro si considera solo l’ampiezza relativa a fotoni polarizzati linearmente e in direzione perpendicolare al piano di scattering.
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De Tollis, B. Dispersive approach to photon-photon scattering. Nuovo Cim 32, 757–768 (1964). https://doi.org/10.1007/BF02735895
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DOI: https://doi.org/10.1007/BF02735895