Bern-Kosower rule for scalar QED

K. Daikouji, M. Shino, Y. Sumino

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


We derive a full Bern-Kosower-type rule for scalar QED starting from quantum field theory: we derive a set of rules for calculating S-matrix elements for any processes at any order of the coupling constant. A gauge-invariant set of diagrams in general is first written in the world line path-integral expression. Then we integrate over x(τ), and the resulting expression is given in terms of a correlation function on the world line 〈x(τ)x(τ′)〉. Simple rules to decompose the correlation function into basic elements are obtained. A gauge transformation known as the integration by parts technique can be used to reduce the number of independent terms before integration over proper-time variables. The surface terms can be omitted provided the external scalars are on shell. Also, we clarify correspondence to the conventional Feynman rule, which enabled us to avoid any ambiguity coming from the infinite dimensionality of the path-integral approach.

Original languageEnglish
Pages (from-to)4598-4615
Number of pages18
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number8
Publication statusPublished - 1996

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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