2008/05/25 by Alexis Licht, A. Lewis Licht, Licht, A. Lewis
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.48550/arxiv.0805.3849
9 pages
arxiv created 2008/05/25 · openalex publication_date 2008/05/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the unparticle action that is made gauge invariant by inclusion of an open Wilson line factor. In deriving vertexes from such an action it has been customary to use a form of differentiating the Wilson line originally proposed by Mandelstam. Using a simple example, we show that the Mandelstam derivative is mathematically inconsistent. We show that there are two ways to define differentiation of the Wilson line. The mathematically consistent method is to differentiate the explicit dependence of the line on the endpoint. The other method is a functional derivative and corresponds in a limiting case to the Mandelstam derivative. We also show that the only path that can be used in the Wilson line integral that leaves the unparticle action both Poincare and scale invariant is the straight line.