Generalized S-matrix in Mixed Representations

Details Generalized S-matrix in Mixed Representations Generalized S-matrix in Mixed Representations

2005-08-30

arxiv.org/abs/hep-ph/0508303v1

Prog.Theor.Phys. 114 (2006) 1201-1234

Physics

High Energy Physics

High Energy Physics - Phenomenology

33 pages, 1 figure

Scientific paper

10.1143/PTP.114.1201

A generalized scattering amplitude where momenta of incoming-particles and outgoing-particles as well as positions of incoming-particles and outgoing-particles are specified is formulated. Idealistic beams and idealistic measuring instruments where momenta and positions satisfy minimum uncertainty are studied with a use of minimum wave packets, coherent states. In the present work, we show general features of the generalized scattering amplitudes based on ${\phi}^4$ theory. We give a proof of completeness of many body states, asymptotic behaviors in the large distance region, and factorization of the amplitudes. Despite of the non-orthogonal properties of wave packets, we found that the probability interpretation is verified. A differential probability depends upon the wave packet size but a total probability that is integrated in the final states is independent from the size of final state wave packet and becomes universal. Few body amplitudes are studied as examples.

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