Progress in Particle Physics pp 711-736 | Cite as

# On the Eikonal Approximation in Quantum Field Theory

## Abstract

In any of the current theories in physics you have to make approximations in calculating experimentally observable quantities: the more complex the system you want to describe the more you have to labour to get reasonable answers. This is obvious for anyone who is involved in theoretical hadron-dynamics or who is tampering with quantum field theory (QFT). If you want to apply this latter theory to high energy reactions, you clearly have to look for an approximation scheme which goes beyond finite-order perturbation theory. One of these schemes is the eikonal approximation [1] which is the subject of this talk.

## Keywords

External Field Transition Matrix Initial Momentum Eikonal Approximation Chain Graph## Preview

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## References and Footnotes

## 1. The number of references to the eikonal method in physics is legion; a few general surveys are

- R.J. Glauber in Lectures in Theoretical Physics, ed. by W.E. Brittin and L.G. Dunham (Interscience Publishers, Inc. New York, (1959)), Volume I, page 315.Google Scholar
- H.D.I. Abarbanel in “Strong Interaction Physics”, International Summer Institute on Theoretical Physics in Kaiserslautern, 1972; Springer 1972.Google Scholar
- H.M. Fried in “Functional Methods and Models in Quantum Field Theory”, The MIT Press, Cambridge, Mass., USA, 1972.Google Scholar

## 2. This formula might be called a relativistic generalisation of the Saxon-Schiff formulae

- D.S. Saxon, L.I. Schiff, Nuovo Cim. 6, 614 (1957).CrossRefMATHMathSciNetGoogle Scholar
- R. Blankenbecler, R.L. Sugar, Phys. Rev. 183, 1387 (1969).CrossRefADSGoogle Scholar
- M. Schlindwein, Diplomarbeit Bonn 1972.Google Scholar
- 3.H. M. Fried, loc. cit. chapter 5.Google Scholar
- 4.A further discussion and generalisation of this formula will be published elsewhere.Google Scholar
- 5.For the simple loop (no external field in the loop) i.e. k = i + 1, the term ℓ
_{k}= n_{k}= 0 in the sum (2.11) contains an F_{−2}which, in turn, is proportional to the Bessel function K_{o}; K_{o}(o) is logarithmically infinite. This is the well-known logarithmic divergence of the loop. For renormalisation we simply replace this first term in the sum (2.11) by a subtraction constant to be suitably chosen.Google Scholar