Quantum Field Theories on Null Surfaces

TL;DR

This paper investigates quantum field theories on null surfaces, revealing finite degrees of freedom in free scalar fields and quantization ambiguities in non-linear sigma models with Wess-Zumino-Witten terms.

Contribution

It demonstrates how quantum field theories behave on null surfaces, identifying quantization ambiguities and duality symmetries that influence the quantization process.

Findings

Free scalar field theory reduces to finite degrees of freedom on null surfaces.

A one-parameter family of inequivalent quantizations exists for free scalar fields.

Quantization ambiguity persists in non-linear sigma models with Wess-Zumino-Witten terms.

Abstract

We study the behaviour of quantum field theories defined on a surface $S$ as it tends to a null surface $S_n$. In the case of a real, free scalar field theory the above limiting procedure reduces the system to one with a finite number of degrees of freedom. This system is shown to admit a one parameter family of inequivalent quantizations. A duality symmetry present in the model can be used to remove the quantum ambiguity at the self-dual point . In the case of the non-linear $\sigma$-model with the Wess-Zumino-Witten term a similar limiting behaviour is obtained. The quantization ambiguity in this case however cannot be removed by any means.