 He has made numerous influential contributions 
in particle and mathematical physics, notably in supercurrent anomalies, higher-spin fields (Curtright field), quantum Liouville theory, geometrostatic sigma models, quantum algebras, and deformation quantization.Curtright is a Fellow of the American Physical Society, a co-recipient (with Charles Thorn) of the SESAPS Jesse Beams Award, a University of Miami Cooper Fellow, and a recipient of the Distinguished Faculty Scholar Award from the University's Senate.He has co-edited and co-authored several books ,
notably on quantum mechanics in phase space.