Scattering theory without largedistance asymptotics: scattering boundary condition
Abstract
By largedistance asymptotics, in conventional scattering theory, at the cost of losing the information of the distance between target and observer, one arrives at an explicit expression for scattering wave functions represented by a scattering phase shift. In the present paper, together with a preceding paper (T. Liu,W.D. Li, and W.S. Dai, JHEP06(2014)087), we establish a rigorous scattering theory without imposing largedistance asymptotics. We show that even without largedistance asymptotics, one can also obtain an explicit scattering wave function represented also by a scattering phase shift, in which, of course, the information of the distance is preserved. Nevertheless, the scattering amplitude obtained in the preceding paper depends not only on the scattering angle but also on the distance between target and observer. In this paper, by constructing a scattering boundary condition without largedistance asymptotics, we introduce a scattering amplitude, like that in conventional scattering theory, depending only on the scattering angle and being independent of the distance. Such a scattering amplitude, when taking largedistance asymptotics, will recover the scattering amplitude in conventional scattering theory. The present paper, with the preceding paper, provides a complete scattering theory without largedistance asymptotics.
 Publication:

arXiv eprints
 Pub Date:
 February 2015
 DOI:
 10.48550/arXiv.1502.00253
 arXiv:
 arXiv:1502.00253
 Bibcode:
 2015arXiv150200253L
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory