Sternberg earned his PhD in 1955 from Johns Hopkins University, with a thesis entitled Some Problems in Discrete Nonlinear Transformations in One and Two Dimensions, supervised by Aurel Wintner.
[12][13][14] In the 1960s, Sternberg became involved with Isadore Singer in the project of revisiting Élie Cartan's papers from the early 1900s on the classification of the simple transitive infinite Lie pseudogroups, and of relating Cartan's results to recent results in the theory of G-structures and supplying rigorous (by present-day standards) proofs of his main theorems.
[citation needed] For instance, together with Bertram Kostant he showed how to use reduction techniques to give a rigorous mathematical treatment of what is known in the physics literature as the BRST quantization procedure.
[18] Together with Victor Guillemin he gave the first rigorous formulation and proof of a hitherto vague assertion about Lie group actions on symplectic manifolds, namely the Quantization commutes with reduction conjecture.
[26] Sternberg worked with Yuval Ne'eman on supersymmetry in elementary particle physics, exploring from this perspective the Higgs mechanism, the method of spontaneous symmetry breaking and a unified approach to the theory of quarks and leptons.