[4] Arthur Jaffe's 30 doctoral students include Joel Feldman, Ezra Getzler, Clifford Taubes, Eugene Wayne, John Imbrie, Christopher King, and Jonathan Weitsman.

He has had many post-doctoral collaborators, including Robert Schrader, Konrad Osterwalder, Juerg Froehlich, Roland Sénéor [fr], Thomas Spencer, Antti Kupiainen, Krzysztof Gawedzki, Tadeusz Balaban, Andrew Lesniewski, Slawomir Klimek, Zhengwei Liu, and Kaifeng Bu.

One of Arthur Jaffe's earliest contributions was his proof, joint with Henry Epstein and Vladimir Glaser, that energy densities in local quantum field theories are always nonpositive.

In a series of landmark papers, Jaffe and collaborators made great progress in understanding the nature of quantum field theory.

Another notable contribution of Jaffe's is his proof, joint with James Glimm and Thomas Spencer, that quantum field theories can have phase transitions.

This work is also notable for using the formalism of reflection positivity to establish its results, which has since become common practice among researchers studying phase transitions in quantum field theory.

Jaffe has made major contributions to the development of this theory, by establishing key examples,[17][18][19][20][21][22][23][24][25] introducing important generalizations,[26][27][28] and providing geometric interpretations.

[31][32][33] Within his work on supersymmetric quantum field theories Jaffe is most known for introducing the JLO cocycle, along with collaborators Andrzej Lesniewski and Konrad Osterwalder.

[34][35] The JLO construction takes as input a supersymmetric quantum field theory (mathematically, a θ-summable spectral triple) and outputs a cocycle in Alain Connes' cyclic cohomology.

In his later years Arthur Jaffe has made varied contributions to the theory of quantum information, along with postdoctoral researchers Zhengwei Liu, Kaifeng Bu, and students.