He is known for his research based on the Haag–Kastler axioms and for his collaboration with Rudolf Haag. With John E. Roberts[5] and Haag, he examined superselection rules in the algebraic quantum field theory, providing the first proof of the spin–statistics theorem entirely based only on first principles. Doplicher and Roberts also proved a reconstruction theorem for the algebra of quantum fields and the compact group of global internal symmetries from the algebra of the observables.[6][7] In other collaborations, Doplicher studied the local aspects of superselection rules. After introducing the split-property, he derived exact current algebras and a weak form of a quantum Noether theorem.[8]
Later in his career, Doplicher dealt with the mathematical foundations of quantum gravity in terms
of the quantum structure of space-time at the Planck scale.[9][10][11] He also addressed the problem of measurement in local quantum physics.[12]
Dell'Antonio, Gianfausto; Doplicher, Sergio; Jona-Lasinio, Giovanni, eds. (1978). Mathematical Problems in Theoretical Physics, International Conference held in Rome. Lecture Notes in Physics. Vol. 80. Springer-Verlag Berlin Heidelberg. doi:10.1007/3-540-08853-9. ISBN978-3-540-08853-0.
Connes, Alain; et al. (2004). Doplicher, Sergio; Longo, Roberto (eds.). Noncommutative Geometry, CIME Summer School Lectures held in Martina Franca, Italy. Lecture Notes in Mathematics. Vol. 1831. Springer-Verlag Berlin Heidelberg. doi:10.1007/b94118. ISBN978-3-540-20357-5.
Others
Doplicher, Sergio; Ferro-Luzzi, Fausta (2011). Il De Rerum Natura di Giorgione, il teatro di Giovanni Bellini e lo sguardo della Gioconda (in Italian). Rome: Aracne. ISBN978-8854841864.
Doplicher, Sergio (2014). O sol che sani ogne vista turbata, Note sulla Ragione nella Divina Commedia (in Italian). Rome: Edicampus. ISBN978-8897591146.
Doplicher, Sergio (2018). Mondo quantistico e Umanesimo (in Italian). Rome: Carocci editore. ISBN9788843093991.
^Doplicher, Sergio (1990). "Abstract compact group duals, operator algebras and quantum field theory". In: Proceedings of the International Congress of Mathematicians, Kyoto, 1990. Vol. 1. pp. 1319–1333.