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Improved automated lattice perturbation theory in background field gauge

T.C. Hammant, R.R. Horgan, C.J. Monahan, A.G. Hart, E.H. Muller, A. Gray, K. Sivalingham, G.M. von Hippel
DAMTP, CMS, University of Cambridge, Cambridge CB3 0WA, U.K.
arXiv:1011.2696 [hep-lat] (11 Nov 2010)

@article{2010arXiv1011.2696H,

   author={Hammant}, T.~C. and {Horgan}, R.~R. and {Monahan}, C.~J. and {Hart}, A.~G. and {M{“u}ller}, E.~H. and {Gray}, A. and {Sivalingham}, K. and {von Hippel}, G.~M.},

   title={“{Improved automated lattice perturbation theory in background field gauge}”},

   journal={ArXiv e-prints},

   archivePrefix={“arXiv”},

   eprint={1011.2696},

   primaryClass={“hep-lat”},

   keywords={High Energy Physics – Lattice, Physics – Computational Physics},

   year={2010},

   month={nov},

   adsurl={http://adsabs.harvard.edu/abs/2010arXiv1011.2696H},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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We present an algorithm to automatically derive Feynman rules for lattice perturbation theory in background field gauge. Vertices with an arbitrary number of both background and quantum legs can be derived automatically from both gluonic and fermionic actions. The algorithm is a generalisation of our earlier algorithm based on prior work by L”uscher and Weisz. We also present techniques allowing for the parallelisation of the evaluation of the often rather complex lattice Feynman rules that should allow for efficient implementation on GPUs, but also give a significant speed-up when calculating the derivatives of Feynman diagrams with respect to external momenta.
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