He was in the lineage of Ph.D. dissertation advisors, starting with Josef Stefan, Ludwig Boltzmann, Paul Ehrenfest, George Uhlenbeck, Emil Konopinski, E. Greuling, and P. F.

[3] Zweifel worked at the Knolls Atomic Power Laboratory as a physicist and a manager of theoretical physics,[4] where he did research on the theory of the slowing down and thermalization of neutrons from mid-1953 to 1958.

[4] He began working with Kenneth M. Case, a physicist who made pioneering contributions to neutron transport theory during the Manhattan Project.

[1] The mathematical approach of Case and Zweifel enables a more direct solution to problems of the type analyzed by Boris Davison in his monograph Neutron Transport Theory and that of Subrahmanyan Chandrasekhar in his treatise Radiative Transfer.

[3][5] During a sabbatical year from the University of Michigan spent as a Visiting Professor at the Middle East Technical University in 1964–1965, Paul and physicist Erdal İnönü organized a two-week NATO Advanced Study Institute on Transport Theory held in Ankara, Turkey.

[1] As of 2024, there have been 27 meetings—none affiliated with any professional society—that were held in the United States, Italy, China, Brazil, Sweden, Russia, England, Hungary and France; Paul hosted six of the conferences in Blacksburg.

[3] Because he studied music beginning when he was four years old, took voice lessons as a youngster, and later performed as a vocalist,[13] he taught an opera course at Virginia Tech after his retirement.