Infrared and high energy fixed angle domains of scattering and the role of eikonal approximation: H. Banerjee and S. K. Sharma, Saha Institute of Nuclear Physics, Calcutta-700009, India

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 84 KB
• Volume: 116
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(78)90242-7

✦ Synopsis

A semiclassical approximation of Feynman's path integral is derived which, in contradistinction to conventional formulae, remains finite in conjugate (focal) points and on caustics, exhibits the experimentally observed oscillatory behavior near these and reduces to familiar approximations far away. The approximative path integral is proportional to a generalized Airy integral governed by a Thorn catastrophe polynomial whose bifurcation properties correspond to those of the solutions of Euler-Lagrange equations. The result is illustrated by computing the propagator of the quantized anharmonic oscillator.