Quantum field theories on null surfaces (Q2724872)

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.