Date of Award
M.S. in Physics
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.
Gao, Caixia, "The Legendre Transform of the Holst Action" (2012). Electronic Theses and Dissertations. 116.