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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. We also discuss several immediate applications.
The dynamics of interacting quantum systems in the presence of disorder is studied and an exact representation for disorder-averaged quantities via Ito stochastic calculus is obtained. The stochastic integral representation affords many advantages, i
The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central charge of the a
We study the decimation to a sublattice of half the sites, of the one-dimensional Dyson-Ising ferromagnet with slowly decaying long-range pair interactions of the form $frac{1}{{|i-j|}^{alpha}}$, in the phase transition region (1< $alpha leq$ 2, and
The Casimir force and free energy at low temperatures has been the subject of focus for some time. We calculate the temperature correction to the Casimir-Lifshitz free energy between two parallel plates made of dielectric material possessing a consta
The low-temperature asymptotic expressions for the Casimir interaction between two real metals described by Leontovich surface impedance are obtained in the framework of thermal quantum field theory. It is shown that the Casimir entropy computed usin