Yang-Mills flow in 1+1 dimensions coupled with a scalar field
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Date
2015-01-07
Authors
Mikula, Paul
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Abstract
We define a Yang-Mills model in 1+1 dimensions coupled to a real scalar field and we
study the Yang-Mills flow equations for this simple model. Yang-Mills flows have not
been thoroughly studied, especially in a physical context, but may be able to provide
valuable insight into both particle physics as well as gravity. We study our model using
both the Hamiltonian equations and Euler-Lagrange equations, and we calculate the
flow numerically using a simple finite difference method for the case of an Abelian Lie
group and static fields. We are able to find several analytic solutions to the equations
of motion and the numerical calculation of the flow suggests most non-constant solutions
are unstable. We also find that the flow depends upon the relative values of the coupling
constant and the mass of the scalar field. The results found with this simple model provide
a starting point for the study of Yang-Mills flow in the context of more complicated (but
more physical) models such as the Abelian Higgs.
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Keywords
Gradient Flow, Gauge Fields