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W. I. Newman (University of California, Los Angeles), Michael Efroimsky (U. S. Naval Observatory, Washington)
Gauge freedom emerges when the number of mathematical variables exceeds the number of physical degrees of freedom and, thus, generates a continuous group of physically-equivalent reparametrisations of the theory. This internal freedom may be interconnected with freedom of coordinate-frame choice (e.g., general relativity) or may be totally independent (e.g., electrodynamics and quantum physics). Previously, we explained how gauge-type freedom emerges in ordinary differential equations whenever the variation-of-constants method is employed, and how this freedom relates to multiple time scales. We illustrated this by examples from linear and nonlinear dynamics.
In orbital mechanics gauge-type freedom emerges when we relax the Lagrange constraint and, thus, model the perturbed trajectory by a sequence of instantaneous Kepler ellipses that are not tangent to the trajectory. It has been shown that this approach is highly beneficial in problems related to orbiting a precessing or non-precessing primary. Other examples emerge in the motion of a body of a variable mass as well as by orbital motion with relativistic effects
We provide an intuitive explanation for what gauge freedom offers in terms of adapting to comoving frames. In celestial mechanics there exists a subtle interplay between the freedom of gauge and the freedom of frame choice, though these freedoms are essentially of a different nature.
We provide a number of other examples of gauge-type freedom being used to simplify practical calculations. These examples range from stochastic problems to electromagnetism. In particular, we focus upon gauge-type freedom emerging in problems characterised by a separatrix and a homoclinic point, and thereby have an unstable manifold. We show that symplectic splitting methods also share gauge freedom. Since a convenient gauge choice, combined with the choice of a comoving frame, simplifies the underlying mathematics, this freedom has the potential to simplify calculations in many physical problems.
The author(s) of this abstract have provided an email address for comments about the abstract: win@ucla.edu
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Bulletin of the American Astronomical Society, 36 #2
© 2004. The American Astronomical Soceity.