On gauge transforms of autonomous ordinary differential equations
Giuseppe Gaeta, Sebastian Walcher
TL;DR
This paper explores gauge transforms in autonomous first-order ODEs, focusing on their mathematical properties and identifying conditions under which nonautonomous ODEs are gauge transforms of autonomous systems.
Contribution
It provides a mathematical analysis of gauge transforms in autonomous ODEs and characterizes nonautonomous ODEs that are gauge equivalents of autonomous systems.
Findings
Characterization of gauge transforms in autonomous ODEs
Conditions for nonautonomous ODEs to be gauge transforms of autonomous systems
Mathematical properties of gauge transforms in differential equations
Abstract
The notion of gauge transform has its origin in Physics (Field Theory). In the present note we discuss -- from a purely mathematical perspective -- special gauge transforms of autonomous first order ODE's and their special properties. Particular attention is given to the problem of identifying those nonautonomous ODE's which are gauge transforms of autonomous systems.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Nonlinear Waves and Solitons · Quantum and Classical Electrodynamics