# Unitary evolution of a pair of Unruh-DeWitt detectors calculated efficiently to an arbitrary perturbative order. (arXiv:1608.08274v3 [hep-th] UPDATED)

Unruh-DeWitt Hamiltonian couples a scalar field with a two-level atom serving

as a particle detector model. Two such detectors held by different observers

following general trajectories can be used to study entanglement behavior in

quantum field theory. Lacking other methods, the unitary evolution must be

studied perturbatively which is considerably time-consuming even to a low

perturbative order. Here we completely solve the problem and present a simple

algorithm for a perturbative calculation based on a solution of a system of

linear Diophantine equations. The algorithm runs polynomially with the

perturbative order. This should be contrasted with the number of perturbative

contributions of the scalar phi^4 theory that is known to grow factorially.

Speaking of the phi^4 model, a welcome collateral result is obtained to

mechanically (almost mindlessly) calculate the interacting scalar phi^n theory

without resorting to Feynman diagrams. We demonstrate it on a typical textbook

example of two interacting fields for n=3,4.