From 1966 until his retirement in 2002 he was professor of theoretical physics there. From 1964 to 1966 he was at the Institute for Advanced Study in Princeton. Hepp was also Loeb Lecturer at Harvard and was at the IHÉSouth near Paris.
Hepp worked on relativistic quantum field theory, quantum statistical mechanics, and theoretical laser physics.
In quantum field theory he gave a complete proof of the Bogoliubov–Parasyuk renormalization theorem (Hepp and Wolfhart Zimmermann, called in their honor the BPHZ theorem). Since a research stay 1975/6 at Massachusetts Institute of Technology he also worked in neuroscience (for example, reciprocal effect between movement sensors, visual sense and eye movements with V Henn in Zurich).