On a model of quantum field theory

A model of quantum field theory in an accelerated frame of reference is considered. It was suggested by Unruh that a uniformly accelerated detector in vacuum would perceive a noise with a thermal Gibbsian distribution. However, in justifying the assertion a singular transformation was implicitly performed, and doubts were expressed by some researches. We discuss a model of quantum field theory in an accelerated frame of reference in the two-dimensional spacetime for the wave equation. By using the Mellin transform, we obtain a representation of solutions of the wave equation. The representation includes a dependence on a parameter. The Unruh field corresponds to a singular limit of the representation.