Theoretical and Mathematical Physics

, Volume 4, Issue 1, pp 643–651 | Cite as

Method of functional integration and an eikonal approximation for potential scattering amplitudes

  • V. N. Pervushin
Article
Received:

Conclusions

We have obtained an exact closed expression for the potential scattering amplitude of particles with spin o and 1/2 as a functional integral with respect to trajectories. This has made possible a relatively simple expansion of the amplitude in powers of the small parameter 1/E. The first term of the expansion is an eikonal approximation for the amplitude for scattering through any angle and in the case of dynamically small angles ϕ≫(pR)−1/2 is identical with the Glauber representation.

We have found the asymptotic form of the scattering amplitude for two particles that exchange virtual mesons. A similar result was obtained in [7] by functional integration with respect to the external fields of the exact Green's functions and a subsequent eikonal expansion on the mass shell. The equivalence of this more accurate method to the approximation described in the present paper (see also [8, 9]) is connected with the interesting problem of the commutativity of the operations of eikonal approximation and second quatization.

If the latter do commute, the Glauber representation for the amplitude (18) in quantum field theory is a consequence of the eikonal approximation in quantum mechanics.

Keywords

Field Theory Quantum Mechanic Small Angle Small Parameter External Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Consultants Bureau, a division of Plenum Publishing Corporation 1971

Authors and Affiliations

  • V. N. Pervushin

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