Summary
The familiar Green functions, as well as some relations between them are built up starting from a single functiong(z), analytic in thez-plane with a cut running along the negative real axis, and such thatg*(z)=g(z*). Some spectral representations are discussed.
Riassunto
Si costruiscono le consuete funzioni di Green, ed alcune relazioni fra di loro, a partire da una singola funzioneg(z), analitica nel pianoz con un taglio lungo l’asse reale negativo, e tale cheg*(z)=g(z*). Si discutono alcune rappresentazioni spettrali.
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Literatur
C. G. Bollini, J. J. Giambiagi andA. Gonzáles Domínguez:Journ. Math. Phys.,6, 165 (1965). See alsoG. Feinberg andA. Pais:Phys. Rev.,131, 2724 (1963).
A. Erdélyi:Tables of Integral Transforms, vol. II (New York, 1954).
See for exampleA. O. G. Källén:Dispersion Relations (Paris, 1960), p. 416.
A. Gonzáles Domínguez: private communication, to be published.
This transformation is related to theK-transform, see ref. (2), p. 121.
Ref. (2), p. 125.
Ref. (2), p. 137.
Ref. (2), p. 215.
I. M. Gel’fand andG. E. Shilov:Les Distributions (Paris, 1962), p. 271. From (3) [also p. 285, from (2)].
Ref. (2), p. 24.
A. Erdélyi:Higher Trascendental Functions, vol.2, p. 6 (16), (17) and (7).
Ref. (2), vol.2, p. 216.
Ref. (11), vol.1, p. 2.
Ref. (2), vol.2, p. 129.
Ref. (2), vol.2, p. 25.
Ref. (2), vol.2, p. 225.
Ref. (2), vol.2, p. 63.
Ref. (2), vol.2, p. 48, form (8).
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Bollini, C.G., Giambiagi, J.J. Relations between Green functions. Nuovo Cim 39, 1146–1158 (1965). https://doi.org/10.1007/BF02734546
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DOI: https://doi.org/10.1007/BF02734546