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Full-Text Articles in Physics
Explicit Construction Of First Integrals For The Toda Flow On A Classical Simple Lie Algebra, Patrick Seegmiller
Explicit Construction Of First Integrals For The Toda Flow On A Classical Simple Lie Algebra, Patrick Seegmiller
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
The Toda flow is a generalization of a dynamical system describing the interaction of particles in a one-dimensional crystal. The concepts and energy and conservation are prominent in the study of dynamical systems, and quantities which remain the same over the evolution of a system provide valuable insights into the system’s behavior. In the realm of mathematics these quantities are called first integrals, or integrals of motion. This paper provides a background for study of the Toda flow, a verification of its integrability, and programming code for finding these quantities which remain unchanged over the evolution of the system.
Symmetry Reduction Of Quasi-Free States, Charles G. Torre
Symmetry Reduction Of Quasi-Free States, Charles G. Torre
All Physics Faculty Publications
Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry-reduced CCR algebra and reduced quasi-free state. When the group is compact, this method of symmetry reduction leads to standard results which can be obtained using other methods. When the group is noncompact, the group averaging prescription relies on technically favorable conditions which we delineate. As an example, we consider symmetry reduction of the usual vacuum state for a Klein–Gordon field on Minkowski spacetime by a noncompact subgroup of the Poincaré group consisting of a …