Publisher
Springer Science and Business Media LLC
Subject
Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics
Reference5 articles.
1. H. Lehmann, K. Symanzik andW. Zimmermann:Nuovo Cimento,6, 319 (1957).
2. If, according toR. Haag (Varenna Lectures, 1958), one assumes thatΦ[g]= =∫ (dx)4 g(x)Φ(x) defines a « quasi-localizable » stateΦ[g]|0〉,g(x) being a smooth test-function, causality implies only: <0| [Φ 1(x 1),Φ 2(x 2)]|0〉=0 for (x 1−x 2)2 → −∞.
3. It may be shown that the knowledge of the correspondenceA 0(ζ) →A[A 0, ζ] uniquely definesS(p).
4. Retardation ofA(x) againstA 0(x) can be characterized, in spite of the impossibility of sharp fronts, by the condition: $$\int\limits_{\alpha _0 }^\infty {dx\left| {A(x)} \right.} \left| {^2 } \right. \leqslant \int\limits_{x_0 }^\infty {dx\left| A \right._0 (x)\left| {^2 } \right.} $$ for everyx 0. Arguments similar to those ofVan Kampen (Phys. Rev.,91, 1267 (1953)) show that this condition implies analiticity ofS(p) in the upper half-plane. Therefore strict retardation excludes the occurence of poles on the positive imaginary axis, due to bound states.
5. Cf. Theorem XII, p. 16 inPaley andWiener:Fourier Transforms in the Complex Domain (American Mathematical Society, 1934).
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