Dispersion relations and the causality concept

H. M. Nussenzveig

E. Corinaldesi

Patrick Suppes, Mario Zanotti

Ole Keller

The macroscopic linear light scattering theory is extended to the semiclassical level starting with a general discussion of spatially nonlocal scattering. An inte- gral relation for the gauge invariant transverse vector potential is given, stressing similarities and differences between the so-called photon-eye and electron-eye picture. The linear constitutive relations and the causal response tensor are key elements in the semiclassical light scattering theory. Elastic scattering processes are discussed from first principles by making use of the transverse Feynman propagator and the causal response tensor. In scattering from mesoscopic me- dia, e.g, the causal response tensor is a two-point function in direct space. In the spatial dispersion subfield this tensor becomes a one-point function, depending only on the vectorial distance between given source and observation points. In the spatial dispersion approximation a simple relation can be obtained between the selfconsistent and causal response tensors in the wave-vector-frequency do- main. Next, we turn to the scattering matrix concept in quantum physics. The treatment describes the transition from an initial to a final object-field tensor product. These states are connected by the S -matrix operator. A general ex- pression for this is obtained in the Interaction Picture. The reduced S -matrix which relates in a direct manner to the scattering between selected initial and final photon states is introduced. The chapter is finished by the establishment and a discussion of the weakly relativistic interaction Hamiltonian, a key ele- ment in the S -matrix operator.

Steven K. Blau

D. I. Blokhint︠s︡ev