Schwinger is recognized as one of the greatest physicists of the twentieth century, responsible for much of modern quantum field theory, including a differential form of path integration, and the equations of motion for quantum fields. He developed the first electroweak model, and the first example of confinement in 1+1 dimensions. He is responsible for the theory of multiple neutrinos, Schwinger terms, and the theory of the spin 3/2 field.
Schwinger developed an affinity for Green's functions from his radar work, and he used these methods to formulate quantum field theory in terms of local Green's functions in a relativistically invariant way. This allowed him to unambiguously calculate the first corrections to the electron magnetic moment in quantum electrodynamics. Earlier noncovariant work had arrived at infinite answers, but the extra symmetry in his methods allowed Schwinger to isolate the correct finite corrections. Schwinger developed renormalization, formulating quantum electrodynamics unambiguously to one-loop order.
In the same era, he introduced nonperturbative methods into quantum field theory, by calculating the rate at which electron-positron pairs are created by tunneling in an electric field, a process now known as the Schwinger effect. This effect could not be seen in any finite order in perturbation theory.
Schwinger's foundational work on quantum field theory constructed the modern framework of field correlation functions and their equations of motion. He expressed the Feynman path integral in differential form, a formalism which allowed bosons and fermions to be treated equally for the first time, a differential form of Grassman integration. He gave elegant proofs for the spin-statistics theorem and the CPT theorem, and noted that the field algebra lead to anomalous Schwinger terms in various classical identities, because of short distance singularities. This were foundational results in field theory, instrumental for the proper understanding of anomalies.
In other notable early work, Rarita and Schwinger formulated the abstract Pauli and Fierz theory of the spin 3/2 field in a concrete form, as a vector of Dirac spinors. In order for the spin-3/2 field to interact consistently, some form of supersymmetry is required, and Schwinger later regretted that he had not followed up on this work far enough to discover supersymmetry.
Schwinger discovered that neutrinos come in multiple varieties, one for the electron and one for the muon. Nowadays there is known to be exactly three neutrinos, the third is the partner the tau lepton.
In the 1960s, Schwinger formulated and analyzed what is now known as the Schwinger model, quantum electrodynamics in one space and one time dimension, the first example of a confining theory. He was also the first to suggest an electroweak gauge theory, an SU(2) gauge group spontaneously broken to electromagnetic U(1) at long distances. This was extended by his student Sheldon Glashow into the accepted pattern of electroweak unification. He attempted to formulate a theory of quantum electrodynamics with point magnetic monopoles, a program which met with limited success because monopoles are strongly interacting when the quantum of charge is small.
Having supervised more than seventy doctoral dissertations, Schwinger is known as one of the most prolific graduate advisors in physics. Four of his students won Nobel prizes: Roy Glauber, Benjamin Roy Mottelson, Sheldon Glashow and Walter Kohn (in chemistry).
Schwinger had a mixed relationship with his colleagues, largely because of his source theory. Schwinger considered source theory as a substitute for field theory, although it is only a different point of view, a version of effective field theory. It treats quantum fields as long-distance phenomena, and does not require a well defined continuum limit. Source theory was considered overly formal and lacking in distinctness from quantum field theory, and the criticisms by his Harvard colleagues led Schwinger to leave the faculty in 1972 for UCLA. His work there was further from the mainstream, but he continued to find source theory reformulations of quantum field theoretic results for the rest of his career.
After 1989 Schwinger took a keen interest in the non-mainstream research of low-energy nuclear fusion reactions (AKA cold fusion). He wrote eight theory papers about it. He resigned from the American Physical Society after their refusal to publish his papers. He felt that cold fusion research was being suppressed and academic freedom violated. He wrote: "The pressure for conformity is enormous. I have experienced it in editors’ rejection of submitted papers, based on venomous criticism of anonymous referees. The replacement of impartial reviewing by censorship will be the death of science."
In his last publications, Schwinger proposed a theory of sonoluminescence as a long distance quantum radiative phenomenon associated not with atoms, but with fast-moving surfaces in the collapsing bubble, where there are discontinuities in the dielectric constant. Standard explanations, now supported by experiments, focus on superheated gas atoms inside the bubble as the source of the light, but Schwinger's methods tie back to his old quantum electrodynamic papers.
By contrast, Feynman was more intuitive, believing that the physics could be extracted entirely from the Feynman diagrams, which gave a particle picture. Schwinger commented on Feynman diagrams in the following way,
Like the silicon chips of more recent years, the Feynman diagram was bringing computation to the masses.
Schwinger disliked Feynman diagrams, because he felt that they made the student focus on the particles and forget about local fields, which in his view inhibited understanding. He went so far as to ban them altogether from his class, although he understood them perfectly well and was observed to use them in private.
Despite sharing the Nobel Prize, Schwinger and Feynman had a different approach to quantum electrodynamics and to quantum field theory in general. Feynman used a regulator, while Schwinger was able to formally renormalize to one loop without an explicit regulator. Schwinger believed in the formalism of local fields, while Feynman had faith in the particle paths. They followed each other's work closely, and each respected the other. On Feynman's death, Schwinger described him as
An honest man, the outstanding intuitionist of our age, and a prime example of what may lie in store for anyone who dares to follow the beat of a different drum.