8 citations · 33 across the 17 of their papers we have counts for
18 papers
Quantization of a Particle on a Two-Dimensional Manifold of Constant Curvature
Paul Bracken
The formulation of quantum mechanics on spaces of constant curvature is studied. It is shown how a transition from a classical system to the quantum case can be accomplished by the…
Motion on Constant Curvature Spaces and Quantization Using Noether Symmetries
Paul Bracken
A general approach is presented for quantizing a metric nonlinear system on a manifold of constant curvature. It makes use of a curvature dependent procedure which relies on determ…
Connections of Zero Curvature and Applications to Nonlinear Partial Differential Equations
Paul Bracken
A general formulation of zero curvature connections in a principle bundle is presented and some applications are discussed. It is proved that a related connection based on a prolon…
The Einstein-Hilbert Action Horizons and Connections with Thermodynamics
Paul Bracken
It is shown that the Einstein-Hilbert action can be constructed by minimizing free energy. The entropy used to determine the free energy is determined on the horizon of a black hol…
A Geometric Method to Investigate Prolongation Structures for Differential Systems With Applications to Integrable Systems
Paul Bracken
A type of prolongation structure for several general systems is discussed. They are based on a set of one-forms in which the underlying structure group of the integrability conditi…
Geometric Approaches for Generating Prolongations for Nonlinear Partial Differential Equations
Paul Bracken
The prolongation structure of a two-by-two problem is formulated very generally in terms of exterior differential forms on a standard representation of Pauli matrices. The differen…