Null Surface Quantization and Quantum Field Theory in Asymptotically Flat Space‐Time

A quantum theory of the free scalar, electromagnetic and gravitational fields in a curved asymptotically flat space‐time is developed. It is shown that the Penrose conformal technique makes it possible to reformulate the null infinity quantization as a problem of the quantization on the proper null surface in the corresponding Penrose space. The Schwinger dynamical principle is exploited to derive the corresponding null surface commutation relations. The general covariant and gauge‐independent form of the commutation relations is also given. The existence of the asymptotic symmetry (BMS) group in the asymptotically flat space‐time is used to define uniquely the “in” and “out” vacuum states. The explicit expressions for the S ‐matrix operator and for the S ‐matrix elements in the asymptotically simple space‐time are given. The functional integration method is used to find the expression for the density matrix describing the observations at ∮+ in the weakly asymptotically simple space‐time when the information loss due to the event horizons or the existence of bare singularities is possible. The application of the developed approach to the problem of quantum evaporation of black holes (Hawking effect) is briefly discussed.