Analytic mappings: A new approach to quantum field theory in accelerated frames

A new approach to quantum field theory in two-dimensional accelerated frames is presented, in which classical, quantum, and thermal aspects of the theory are explicitly expressed in terms of analytic mappings. Each analytic function defines an accelerated frame and a quantum production rate associated with it. Conversely, given the quantum production rate, we reconstruct the mapping. Real singularities of the mapping determine the asymptotic regions of the space-time. Each real singularity has an associated temperature. In particular, critical points define event horizons. Temperature appears irrespective of the presence of event horizons. We classify the accelerated frames in terms of the singularities of analytic mappings and their associated quantum production rates and temperatures. It is proved that the only accelerated frame in which particle production takes place in a global thermal equilibrium situation is the Rindler frame. Nevertheless, the Planckian spectrum is not restricted to Rindler observers. Comparison with the existing literature is made. Generalizations of the approach are considered, for instance its extension to four-dimensional curved space-time.