Time-dependent accelerated Unruh-DeWitt detector without event horizon

We investigate unitarily inequivalent representations of the algebra of operators in quantum field theory in the cases where there is a Fock representation of the commutation relations. We examine more closely the operational definition of a measurement device, discussing the Unruh-DeWitt and Glauber models of quantum detectors. The transition probability per unit of proper time of both detectors in different non-inertial frames of reference in Minkowski spacetime is evaluated. We first study detectors traveling in a stationary worldline with a constant proper acceleration, i.e., a hyperbolic motion, interacting with the field prepared in the Poincar\'e invariant Fock vacuum state. Next, we study the Unruh-DeWitt detector at rest in a non-uniformly accelerated frame, with a time dependent acceleration interacting with the field in the Poincar\'e invariant Fock vacuum state. We evaluate the positive frequency Wightman function for the non-uniformly accelerated frame in a finite time interval and find that it is similar to the two-point correlation function of a system in equilibrium with a thermal bath. Calculating the transition rate, the non-uniformly accelerated Unruh-DeWitt detector can be excited even if the scalar field is prepared in the vacuum state.