2010/06/10 by Stefano Capitani, Michael Creutz, Johannes Weber +2
Physics and Astronomy · #Black Holes and Theoretical Physics #Fermion #Lattice (music) #Lorentz transformation #Mathematical physics #Particle physics #Particle physics theoretical and experimental studies #Perturbation theory (quantum mechanics) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Renormalization #Renormalization group #Symmetry breaking #Theoretical physics #Universality (dynamical systems) #Vacuum polarization #hep-lat
paper · pdf · doi:10.1007/jhep09(2010)027
published as JHEP 1009:027,2010 · 23 pages, 1 figure
arxiv created 2010/06/10 · openalex publication_date 2010/09/01 · arxiv updated 2014/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the renormalization properties of minimally doubled fermions, at one loop in perturbation theory. Our study is based on the two particular realizations of Borici-Creutz and Karsten-Wilczek. A common feature of both formulations is the breaking of hyper-cubic symmetry, which requires that the lattice actions are supplemented by suitable counterterms. We show that three counterterms are required in each case and determine their coefficients to one loop in perturbation theory. For both actions we compute the vacuum polarization of the gluon. It is shown that no power divergences appear and that all contributions which arise from the breaking of Lorentz symmetry are cancelled by the counterterms. We also derive the conserved vector and axial-vector currents for Karsten-Wilczek fermions. Like in the case of the previously studied Borici-Creutz action, one obtains simple expressions, involving only nearest-neighbour sites. We suggest methods how to fix the coefficients of the counterterms non-perturbatively and discuss the implications of our findings for practical simulations.