Electronic Theses and Dissertations


Caixia Gao

Date of Award


Document Type


Degree Name

M.S. in Physics

First Advisor

Luca Bombelli

Second Advisor

Alakabha Datta

Third Advisor

Marco Cavaglia

Relational Format



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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