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Showing 1 to 3 of 3 for “"Legendre Transformation"”.
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The Legendre Transform of the Holst Action
… 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 …
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Differential algebraic methods for obtaining approximate numerical solutions to the Hamilton-Jacobi equation
… principle function generates the canonical transformation, or mapping, between the initial and final state of every trajectory through the system. Since the map is represented by a generating function, it must automatically be symplectic, even in the presence of round-off error. The …
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Effective action approach to quantum phase transitions in bosonic lattices
… the underlying effective action is derived via a Legendre transformation. After determining the Ginzburg-Landau expansion of the effective action to first order in the tunneling term. expressions for the Mott insulator-superfluid phase boundary, condensate density, average particle number, and …