Quantum field theories on null surfaces
This paper constructs models in order to examine the theory of quantization on null surfaces. These concepts are important in many field theories and a system of direct interest is the dynamics on the horizon of a black hole; the horizon is the null surface. Initially a flat Minkowskian manifold is considered which is the surface of a cylinder of radius \(r\), so that the metric may be expressed in terms of the variables \(t\), \(z\) and the spanning angle. If \(z\) is taken to be time-dependent so that \(z= vt\) and \(v\to 1\) we obtain the null surface. Real scalar fields are defined which are valued on a circle (the limit as \(v\to 1\) needs to be considered carefully using renormalization). It is found that the quantization leads to a one parameter set of possible fields, that is only unique at a special point called the self-dual point. In general there is ambiguity in the quantization. For a different non-linear model, similarly it is found that the quantization is non-unique.
scientific article; zbMATH DE number 1618327