Text

theses

ETD doctoral

In chapter 1, a rigorous proof is presented of the existence of the static, spherically symmetric spacetime that is the solution of the Einstein field equations coupled with an electric field obeying the equations of electromagnetism of Bopp-Landé-Thomas-Podolsky for a static point charge. It is shown that the electric field energy is finite, just as the case is for this theory on a background flat spacetime. The argument proves the existence of a 2-parameter family of solutions in the regime of large radial variable and of a 1-parameter family when this variable is small, by means of a new technique for estimating the radius of convergence of a power series whose coefficients are defined by a polynomial recursion. The existence of the intersection of the families of solutions from these two regimes is established through carefully restricting the allowable ranges of their parameters so that the Poincaré-Miranda theorem can be applied.

In chapter 2, a generalization of the system of so-called Jacobi coordinate transformations for classical and quantum many-body problems is developed, suitable for the study of questions involving the center-of-mass of the system when the interaction between the bodies enjoys symmetry properties. It is applied to the study of asymptotic ground-state properties of a quantum Hamiltonian that models an atom with N bosonic electrons without the Born-Oppenheimer approximation. The conjectured Hartree limit of N going to infinity is shown to supply a rigorous upper bound to the ground state energy.

ETD_11385

Ph.D.

Includes bibliographical references

doi:10.7282/t3-czsg-4t42

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