A Faddeev-Niemi Solution that Does Not Satisfy Gauss' Law
Jarah Evslin, Simone Giacomelli
TL;DR
This paper presents a specific solution within the Faddeev-Niemi reformulation of SU(2) Yang-Mills theory that fails to satisfy Gauss' law, indicating the reformulation's inequivalence to original Yang-Mills theory.
Contribution
It demonstrates that the Faddeev-Niemi reformulation does not fully replicate SU(2) Yang-Mills theory by providing a solution that violates Gauss' law constraints.
Findings
The solution does not satisfy Gauss' law constraints.
The reformulation describes Yang-Mills with an external charge.
Reformulation is inequivalent to original Yang-Mills theory.
Abstract
Faddeev and Niemi have proposed a reformulation of SU(2) Yang-Mills theory in terms of a U(1) gauge theory with 8 off-shell degrees of freedom. We present a solution to Faddeev and Niemi's formulation which does not solve the SU(2) Yang-Mills Gauss constraints. This demonstrates that the proposed reformulation is inequivalent to Yang-Mills, but instead describes Yang-Mills coupled to a particular choice of external charge.
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