A new diagrammatic methodology for non-relativistic quantum electrodynamics

A new diagrammatic basis is presented for quantum electrodynamical calculations on photonic processes and interactions in atomic and molecular systems. Established through a multi-dimensional representation, in which each dimension signifies photon interactions of a differentiable type, the resultant interaction graphs prove to have advantages over time-ordered diagrams. The representation registers an isomorphism of different photonic interactions, and allows the treatment of all congruent processes within a common framework. Elementary examples are given to exhibit this feature. Principles are delineated for the construction of state-sequence diagrams from the interaction plane graphs. For any given process each such diagram fully embodies the entire set of time-ordered diagrams. Implementation of the method is extensively illustrated for a variety of high-order applications relevant to current laser experimentation. The new methods prove to expedite analysis, affording a highly compact means of conveying information and, in higher-order applications, circumventing the calculational interpretation of an extremely large number of time-ordered diagrams.