Some Applications of the ADM Formalism

TL;DR

This paper explores the ADM formalism in 2+1-dimensional gravity, focusing on its reduction, quantization, and the role of large diffeomorphisms, linking different areas of relativity theory.

Contribution

It demonstrates the relation and quantization of reduced ADM formalism in specific topologies and highlights the significance of large diffeomorphisms in quantum gravity.

Findings

Relation between partially and fully reduced ADM formalism.

Quantization of the formalism in R x T^2 topology.

Illustration of the role of large diffeomorphisms in quantum theory.

Abstract

The ADM Formalism is discussed in the context of 2+1--dimensional gravity, uniting two areas of relativity theory in which Stanley Deser has been particularly active. For spacetimes with topology R x T^2 the partially reduced and fully reduced ADM formalism are related and quantized, and the role of "large diffeomorphisms" (the modular group) in the quantum theory is illustrated.