摘要:

AbstractIn the hope of getting some new insight into the infrared problem we study the space‐time aspects of electron scattering events in quantum electrodynamics. Localization of electrons is provided by „counters”︁ described by a quasilocal field. An initialn‐electron state, prepared in a specified bounded region of space‐time, is obtained by applyingnelectron field operators, smeared over suitable test functions, to the vacuum. The probability thatmcounters localized in bounded four‐dimensional neighbourhoods of the pointsx1, …,xmare triggered, is the vacuum expectation value of a product of two time‐ordered products ofnelectron fields andmcounter fields each. These vacuum expectation values are closely related to the Green's functions of the theory. For macroscopic counter separationsxi–xiwe can evaluate the triggering probability with the help of asymptotic methods, starting from thep‐space singularities of the Green's functions. We assume the singularity structure of perturbation theory summed over soft photons. As typical examples we analyze one and two electron initial states. The results are those expected for classical particles. For a one‐particle state with momentump, prepared in a neighbourhood of the origin, the probability that counters inx1. …,xmare triggered is measurably non‐zero only ifx1, …,xmlie on a ray through O in directionp. The dependence of the probability on the distances ∥xi–xi∥ is as given by geometry. Similar results hold for two‐ particle states, in which case scattering events are seen. Only elastic scattering is considered. The dependence of the scattering probability on the momenta of the four particles involved is given by a factor |M(p, p2,q1, q2)|2.Mreplaces theS‐matrix element of the familiar case without infrared problems. The definition ofMis a generalization of the reduction formula expression ofSin terms of Green's functions. The properties ofMare not discussed. Processes involving photons a

ISSN:0015-8208    

DOI:10.1002/prop.19740220702

出版商:WILEY‐VCH Verlag    

年代:1974

数据来源: WILEY

ISSN:0015-8208    

DOI:10.1002/prop.19740220703

出版商:WILEY‐VCH Verlag    

年代:1974

数据来源: WILEY

ISSN:0015-8208    

DOI:10.1002/prop.19740220701

出版商:WILEY‐VCH Verlag    

年代:1974

数据来源: WILEY