Summary
It is shown that the vertex functionΓ(p 1,p 2) in quantized field theories has to satisfy a condition which implies that it vanishes for large momenta. This condition follows from the requirement that no abnormal states (with negative norm) exist.
Riassunto
Si dimostra che la funzione di verticeΓ(p 1,p 2) nelle teorie di campo quantistiche deve soddisfare una condizione per la quale la funzione deve annullarsi per quantità di moto elevate. Tale condizione è conseguenza della esigenza che non esistano stati abnormi (con norma negativa).
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References
T. D. Lee:Phys. Rev.,95, 1329 (1954).
G. Källén undW. Pauli:Dan. Mat. Fys. Medd. Im Druck.
Vgl. z.B.H. Lehmann:Nuovo Cimento,11, 342 (1954).
H. Lehmann, K. Symanzik undW. Zimmermann:Nuovo Cimento,1, 205 (1955).
Dieser Umstand ist bereits von Källén zur Abschätzung von Renormierungskonstanten benutzt worden.G. Källén:Dan. Mat. Fys. Medd.,27, n. 12 (1953).
Zunächst folgt Gl. (7) nur fürk 0 > 0. Durch Vertauschung vonx undy in Gl. (4) sieht man jedoch, daß (7) für alle Frequenzen gilt.
Solche Ausdrücke sind des öfteren benutzt worden, z.B. vonN. Hu:Phys. Rev.,80, 1109 (1950);R. Karplus et al.:Phys. Rev.,90, 1072 (1953);K. A. Brueckner et al.,Phys. Rev.,90, 476 (1953);G. Feldman,Proc. Roy. Soc. London, A223, 112 (1954).
D. V. Widder:The Laplace Transform (Princeton, 1946), Chapt. VIII.
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Lehmann, H., Symanzik, K. & Zimmermann, W. Zur Vertexfunktion in quantisierten Feldtheorien. Nuovo Cim 2, 425–432 (1955). https://doi.org/10.1007/BF02826501
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DOI: https://doi.org/10.1007/BF02826501