Electronic Theses and Dissertations

Title

The Legendre Transform of the Holst Action

Author

Caixia Gao

Date of Award

2012

Document Type

Dissertation

Degree Name

M.S. in Physics

First Advisor

Luca Bombelli

Second Advisor

Alakabha Datta

Third Advisor

Marco Cavaglia

Abstract

I start with a short introduction on 3+1 ADM form and the tetrad form of General Relativity, then I review the Legendre transform of the Einstein-Hilbert action and the Palatini action. The Holst action is a generalization of the Palatini action by including a topological term. I derive Ashtekar's connection form directly from this action by doing the Legendre transformation rather than by a canonical transformation in the usual phase space. This is done in both Remmanian signature with half-flat connection and Lorentz signature with general Barbero-Immirzi parameter.

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