☰ Notes

Classical 2+1 D Gravity

It has beenm a long time since people starts to work on quantizing gravitational field. And lower dimensional gravity provides us a good playground to test various ideas and methods.

In particular, 2+1 dimensional gravity has been studied extensively since it is much simpler than the physical 3+1 dimensional case, yet still shares many important features.

Chern-Simons Formulation

It has been revealed that the 2+1 dimensional gravity can be reformulated as a Chern-Simons gauge theory:

  • 1988-12witten One of the first attempts to reformulate 2+1 dimensional gravity as a Chern-Simons theory and quantize it.

Classical Phase Space

It is commonly used to study the 2+1 dimensional gravity using a constriant first quantization. Thus, it is important to understand the classical phase space of the theory. Several papers give detailed discussions on this topic:

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