An integral-free representation of the Dyson series using divided differences

Understand

The Dyson series is an infinite sum of multi-dimensional time-ordered integrals, which serves as a formal representation of the quantum time-evolution operator in the interaction-picture.

• Using the mathematical tool of divided differences, we introduce an alternative representation for the series that is entirely free from both time ordering and integrals.
• In this new formalism, the Dyson expansion is given as a sum of efficiently-computable divided differences of the exponential function, considerably simplifying the calculation of the Dyson expansion terms, while also allowing for time-dependent perturbation calculations to be performed directly in the Schr{\"o}dinger-picture.
• We showcase the utility of this novel representation by studying a number of use cases.