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On the connection between the vertex function in coordinate space and in momentum space (I). Formalism

Authors
Journal
Nuclear Physics B
0550-3213
Publisher
Elsevier
Publication Date
Volume
62
Identifiers
DOI: 10.1016/0550-3213(73)90264-2

Abstract

Abstract Formulas are derived which represent the coordinate space matrix elements of products of two field operators between the vacuum state and a state with sharp energy-momentum in terms of boundary values of the momentum space vertex function. The assumptions behind the results are (i) the general physical assumptions of a Wightman field theory and (ii) some moderate boundedness properties of the momentum space vertex function. The formulas will be used in an accompanying paper to investigate to what extent the coordinate space light cone singularities determine the momentum space structure. The resulting formulas closely resemble the corresponding two-point results. They contain mass integrals over the well-known distribution Δ 2 +, this time, however, modified by complex exponentials depending upon the external energy-momentum vector.

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