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Julian Schwinger | |
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Born | Julian Seymour Schwinger February 12, 1918 New York City, New York, U.S. |

Died | July 16, 1994 76) Los Angeles, California, U.S. | (aged

Nationality | United States |

Alma mater | City College of New York Columbia University |

Known for | Quantum electrodynamics Spin–statistics theorem Sigma model MacMahon Master theorem List of things named after Julian Schwinger |

Spouse(s) | Clarice Carrol (m. 1947) |

Awards | Albert Einstein Award (1951) National Medal of Science (1964) Nobel Prize in Physics (1965) |

Scientific career | |

Fields | Physics |

Institutions | University of California, Berkeley Purdue University Massachusetts Institute of Technology Harvard University University of California, Los Angeles |

Doctoral advisor | Isidor Isaac Rabi |

Doctoral students | Roy Glauber Ben R. Mottelson Eugen Merzbacher Sheldon Lee Glashow Walter Kohn Bryce DeWitt Daniel Kleitman Sam Edwards Gordon Baym Lowell S. Brown Stanley Deser Lawrence Paul Horwitz Margaret G. Kivelson Tung-Mow Yan |

**Julian Seymour Schwinger** ( /ˈʃwɪŋər/ ; February 12, 1918 – July 16, 1994) was a Nobel Prize winning American theoretical physicist. He is best known for his work on the theory of quantum electrodynamics (QED), in particular for developing a relativistically invariant perturbation theory, and for renormalizing QED to one loop order. Schwinger was a physics professor at several universities.

The **Nobel Prize** is a set of annual international awards bestowed in several categories by Swedish and Norwegian institutions in recognition of academic, cultural, or scientific advances.

The **United States of America** (**USA**), commonly known as the **United States** or **America**, is a country comprising 50 states, a federal district, five major self-governing territories, and various possessions. At 3.8 million square miles, the United States is the world's third or fourth largest country by total area and is slightly smaller than the entire continent of Europe's 3.9 million square miles. With a population of over 327 million people, the U.S. is the third most populous country. The capital is Washington, D.C., and the largest city by population is New York City. Forty-eight states and the capital's federal district are contiguous in North America between Canada and Mexico. The State of Alaska is in the northwest corner of North America, bordered by Canada to the east and across the Bering Strait from Russia to the west. The State of Hawaii is an archipelago in the mid-Pacific Ocean. The U.S. territories are scattered about the Pacific Ocean and the Caribbean Sea, stretching across nine official time zones. The extremely diverse geography, climate, and wildlife of the United States make it one of the world's 17 megadiverse countries.

A **theory** is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking. Depending on the context, the results might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.

- Biography
- Career
- Schwinger and Feynman
- Death
- See also
- Selected publications
- References
- Further reading
- External links

Schwinger is recognized as one of the greatest physicists of the twentieth century, responsible for much of modern quantum field theory, including a variational approach, 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.

The **Schwinger's quantum action principle** is a variational approach to quantum mechanics and quantum field theory. This theory was introduced by Julian Schwinger. In this approach, the **quantum action** is an operator. Although it is superficially different from the path integral formulation where the action is a classical function, the modern formulation of the two formalisms are identical.

Julian Seymour Schwinger was born in New York City, to Jewish parents originally from Poland, Belle (née Rosenfeld) and Benjamin Schwinger, a garment manufacturer,^{ [1] } who had migrated to America. Both his father and his mother's parents were prosperous clothing manufacturers, although the family business declined after the Wall Street Crash of 1929. The family followed the Orthodox Jewish tradition. Schwinger attended the Townsend Harris High School and then the City College of New York as an undergraduate before transferring to Columbia University, where he received his B.A. in 1936 and his Ph.D. (overseen by Isidor Isaac Rabi) in 1939 at the age of 21. He worked at the University of California, Berkeley (under J. Robert Oppenheimer), and was later appointed to a position at Purdue University.

**Ashkenazi Jews**, also known as **Ashkenazic Jews** or simply **Ashkenazim**, are a Jewish diaspora population who coalesced in the Holy Roman Empire around the end of the first millennium.

The **Wall Street Crash of 1929**, also known as the **Stock Market Crash of 1929** or the **Great Crash**, was a major stock market crash that occurred in late October 1929. It started on October 24 and continued until October 29, 1929, when share prices on the New York Stock Exchange collapsed.

**Townsend Harris High School** (THHS) is a public magnet high school for the humanities in the borough of Queens in New York City. Students and alumni often refer to themselves as "Harrisites." Townsend Harris consistently ranks as among the top 100 High Schools in the United States. Its most recent *U.S. News and World Report* ranking in 2019 puts THHS at #1 in New York City, #1 in New York State and #11 in the nation.

After having worked with Oppenheimer, Schwinger's first regular academic appointment was at Purdue University in 1941. While on leave from Purdue, he worked at the Radiation Laboratory at MIT instead of at the Los Alamos National Laboratory during World War II. He provided theoretical support for the development of radar. After the war, Schwinger left Purdue for Harvard University, where he taught from 1945 to 1974. In 1966 he became the Eugene Higgins professor of physics at Harvard.

**Purdue University** is a public research university in West Lafayette, Indiana, and the flagship campus of the Purdue University system. The university was founded in 1869 after Lafayette businessman John Purdue donated land and money to establish a college of science, technology, and agriculture in his name. The first classes were held on September 16, 1874, with six instructors and 39 students.

The **Massachusetts Institute of Technology** (**MIT**) is a private research university in Cambridge, Massachusetts. Founded in 1861 in response to the increasing industrialization of the United States, MIT adopted a European polytechnic university model and stressed laboratory instruction in applied science and engineering. It has since played a key role in the development of many aspects of modern science, engineering, and mathematics, and is widely known for its innovation and academic strength, making it one of the most prestigious institutions of higher learning in the world. The Institute is a land-grant, sea-grant, and space-grant university, with an urban campus that extends more than a mile alongside the Charles River.

**Los Alamos National Laboratory** is a United States Department of Energy national laboratory initially organized during World War II for the design of nuclear weapons as part of the Manhattan Project. It is located a short distance northwest of Santa Fe, New Mexico in the southwestern United States.

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 calculate unambiguously the first corrections to the electron magnetic moment in quantum electrodynamics. Earlier non-covariant work had arrived at infinite answers, but the extra symmetry in his methods allowed Schwinger to isolate the correct finite corrections.

In mathematics, a **Green's function** of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions is its impulse response.

In particle physics, **quantum electrodynamics** (**QED**) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.

Schwinger developed renormalization, formulating quantum electrodynamics unambiguously to one-loop order.

**Renormalization** is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of quantities to compensate for effects of their **self-interactions**. However, even if it were the case that no infinities arise in loop diagrams in quantum field theory, it can be shown that renormalization of mass and fields appearing in the original Lagrangian is necessary.

In the same era, he introduced non-perturbative 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. His approach started with a quantum action and allowed bosons and fermions to be treated equally for the first time, using 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 led to anomalous Schwinger terms in various classical identities, because of short distance singularities. These 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 are known to be three light neutrinos; the third is the partner of 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 73 doctoral dissertations ,^{ [2] } 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, because he always pursued independent research, different from mainstream fashion. In particular, Schwinger developed the source theory,^{ [3] } a phenomenological theory for the physics of elementary particles, which is a predecessor of the modern effective field theory. It treats quantum fields as long-distance phenomena and uses auxiliary 'sources' that resemble currents in classical field theories. The source theory is a mathematically consistent field theory with clearly derived phenomenological results. The criticisms by his Harvard colleagues led Schwinger to leave the faculty in 1972 for UCLA. It is a story widely told that Steven Weinberg, who inherited Schwinger's paneled office in Lyman Laboratory, there found a pair of old shoes, with the implied message, "think you can fill these?". At UCLA, and for the rest of his career, Schwinger continued to develop the source theory and its various applications.

After 1989 Schwinger took a keen interest in the non-mainstream research of cold fusion. He wrote eight theory papers about it. He resigned from the American Physical Society after their refusal to publish his papers.^{ [4] } 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. The mechanism of sonoluminescence now supported by experiments focuses on superheated gas inside the bubble as the source of the light.^{ [5] }

Schwinger was jointly awarded the Nobel Prize in Physics in 1965 for his work on quantum electrodynamics (QED), along with Richard Feynman and Shin'ichirō Tomonaga. Schwinger's awards and honors were numerous even before his Nobel win. They include the first Albert Einstein Award (1951), the U.S. National Medal of Science (1964), honorary D.Sc. degrees from Purdue University (1961) and Harvard University (1962), and the Nature of Light Award of the U.S. National Academy of Sciences (1949).

As a famous physicist, Schwinger was often compared to another legendary physicist of his generation, Richard Feynman. Schwinger was more formally inclined and favored symbolic manipulations in quantum field theory. He worked with local field operators, and found relations between them, and he felt that physicists should understand the algebra of local fields, no matter how paradoxical it was. 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.

^{ [6] }^{ [7] }

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. The true difference is however deeper, and it was expressed by Schwinger in the following passage,

Eventually, these ideas led to Lagrangian or action formulations of quantum mechanics, appearing in two distinct but related forms, which I distinguish as

differential and integral. The latter, spearheaded by Feynman has had all the press coverage, but I continue to believe that the differential viewpoint is more general, more elegant, more useful.^{ [8] }

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.

^{ [9] }

Schwinger died of pancreatic cancer. He is buried at Mount Auburn Cemetery; is engraved above his name on his tombstone. These symbols refer to his calculation of the correction ("anomalous") to the magnetic moment of the electron.

- Schwinger, J (1948). "On Quantum-Electrodynamics and the Magnetic Moment of the Electron".
*Phys. Rev*.**73**(4): 416–417. Bibcode:1948PhRv...73..416S. doi:10.1103/PhysRev.73.416. - Schwinger, J (1948). "Quantum Electrodynamics. I. A Covariant Formulation".
*Phys. Rev*.**74**(10): 1439–1461. Bibcode:1948PhRv...74.1439S. doi:10.1103/PhysRev.74.1439. - Schwinger, J (1949). "Quantum Electrodynamics. II. Vacuum Polarization and Self-Energy".
*Phys. Rev*.**75**(4): 651–679. Bibcode:1949PhRv...75..651S. doi:10.1103/PhysRev.75.651. - Schwinger, J (1949). "Quantum Electrodynamics. III. The Electromagnetic Properties of the Electron Radiative Corrections to Scattering".
*Phys. Rev*.**76**(6): 790–817. Bibcode:1949PhRv...76..790S. doi:10.1103/PhysRev.76.790. - Feshbach, H., Schwinger, J. and J. A. Harr. "Effect of Tensor Range in Nuclear Two-Body Problems", Computation Laboratory of Harvard University, United States Department of Energy (through predecessor agency the Atomic Energy Commission) (November 1949).
- Schwinger, J (1951). "On Gauge Invariance and Vacuum Polarization".
*Phys. Rev*.**82**(5): 664–679. Bibcode:1951PhRv...82..664S. doi:10.1103/PhysRev.82.664. - Schwinger, J. "On Angular Momentum", Harvard University, Nuclear Development Associates, Inc., United States Department of Energy (through predecessor agency the Atomic Energy Commission) (January 26, 1952).
- Schwinger, J. "The Theory of Quantized Fields. II", Harvard University, United States Department of Energy (through predecessor agency the Atomic Energy Commission) (1951).
- Schwinger, J. "The Theory of Quantizied Fields. Part 3", Harvard University, United States Department of Energy (through predecessor agency the Atomic Energy Commission) (May 1953).
- Schwinger, J.
*Einstein's Legacy*(1986). Scientific American Library.

**Richard Phillips Feynman** was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics for which he proposed the parton model. For contributions to the development of quantum electrodynamics, Feynman received the Nobel Prize in Physics in 1965 jointly with Julian Schwinger and Shin'ichirō Tomonaga.

In physics, the **fine-structure constant**, also known as **Sommerfeld's constant**, commonly denoted by *α*, is a dimensionless physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles. It is related to the elementary charge *e*, which characterizes the strength of the coupling of an elementary charged particle with the electromagnetic field, by the formula 4π*ε*_{0}*ħcα* = *e*^{2}. As a dimensionless quantity, it has the same numerical value in all systems of units, which is approximately 1/137. The inverse of *α* is 137.035999084(21).

**Zero-point energy** (**ZPE**) is the difference between the lowest possible energy that a quantum mechanical system may have, and the classical minimum energy of the system. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state due to the Heisenberg uncertainty principle. As well as atoms and molecules, the empty space of the vacuum has these properties. According to quantum field theory, the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields, whose quanta are fermions, and force fields, whose quanta are bosons. All these fields have zero-point energy. These fluctuating zero-point fields lead to a kind of reintroduction of an aether in physics, since some systems can detect the existence of this energy. However this aether cannot be thought of as a physical medium if it is to be Lorentz invariant such that there is no contradiction with Einstein's theory of special relativity.

**Steven Weinberg** is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles.

**Shinichiro Tomonaga**, usually cited as **Sin-Itiro Tomonaga** in English, was a Japanese physicist, influential in the development of quantum electrodynamics, work for which he was jointly awarded the Nobel Prize in Physics in 1965 along with Richard Feynman and Julian Schwinger.

In theoretical physics, the **renormalization group** (**RG**) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying force laws as the *energy scale* at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle.

In physics, the **Schwinger model**, named after Julian Schwinger, is the model describing 2D *Euclidean* quantum electrodynamics with a Dirac fermion. This model exhibits a spontaneous symmetry breaking of the U(1) symmetry due to a chiral condensate due to a pool of instantons. The photon in this model becomes a massive particle at low temperatures. This model can be solved exactly and is used as a toy model for other more complex theories.

**Kenneth Geddes** "**Ken**" **Wilson** was an American theoretical physicist and a pioneer in leveraging computers for studying particle physics. He was awarded the 1982 Nobel Prize in Physics for his work on phase transitions—illuminating the subtle essence of phenomena like melting ice and emerging magnetism. It was embodied in his fundamental work on the renormalization group.

In particle physics, **asymptotic freedom** is a property of some gauge theories that causes interactions between particles to become asymptotically weaker as the energy scale increases and the corresponding length scale decreases.

In physics, the **Landau pole** is the momentum scale at which the coupling constant of a quantum field theory becomes infinite. Such a possibility was pointed out by the physicist Lev Landau and his colleagues. The fact that couplings depend on the momentum scale is the central idea behind the renormalization group.

**Stochastic electrodynamics** (**SED**) is an extension of the de Broglie–Bohm interpretation of quantum mechanics, with the electromagnetic zero-point field (ZPF) playing a central role as the guiding pilot-wave. The theory is a deterministic nonlocal hidden-variable theory. It is distinct from other more mainstream interpretations of quantum mechanics such as QED, a stochastic electrodynamics of the Copenhagen interpretation and Everett's many-worlds interpretation. SED describes energy contained in the electromagnetic vacuum at absolute zero as a stochastic, fluctuating zero-point field. The motion of a particle immersed in this stochastic zero-point radiation generally results in highly nonlinear, sometimes chaotic or emergent, behaviour. Modern approaches to SED consider the quantum properties of waves and particles as well-coordinated emergent effects resulting from deeper (sub-quantum) nonlinear matter-field interactions.

In quantum field theory, and specifically quantum electrodynamics, **vacuum polarization** describes a process in which a background electromagnetic field produces virtual electron–positron pairs that change the distribution of charges and currents that generated the original electromagnetic field. It is also sometimes referred to as the **self-energy** of the gauge boson (photon).

In particle physics, the **history of quantum field theory** starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Major advances in the theory were made in the 1940s and 1950s, and led to the introduction of renormalized quantum electrodynamics (QED). QED was so successful and accurately predictive that efforts were made to apply the same basic concepts for the other forces of nature. By the late 1970s, these efforts successfully utilized gauge theory in the strong nuclear force and weak nuclear force, producing the modern standard model of particle physics.

In quantum electrodynamics, the **anomalous magnetic moment** of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle.

The first **Shelter Island Conference** on the Foundations of Quantum Mechanics was held from June 2–4, 1947 at the Ram's Head Inn in Shelter Island, New York. Shelter Island was the first major opportunity since Pearl Harbor and the Manhattan Project for the leaders of the American physics community to gather after the war. As Julian Schwinger would later recall, "It was the first time that people who had all this physics pent up in them for five years could talk to each other without somebody peering over their shoulders and saying, 'Is this cleared?'"

**Steven C. Frautschi** is an American theoretical physicist, currently professor of physics emeritus at the California Institute of Technology (Caltech). He is known principally for his contributions to the bootstrap theory of the strong interactions and for his contribution to the resolution of the infrared divergence problem in quantum electrodynamics (QED). He was named a Fellow of the American Physical Society in 2015 for "contributions to the introduction of Regge poles into particle physics, elucidation of the role of infrared photons in high energy scattering, and for seminal contributions to undergraduate physics education".

**Norman Myles Kroll** was an American theoretical physicist, known for his pioneering work in QED.

**Laurie Mark Brown** is an American theoretical physicist and historian of quantum field theory and elementary particle physics.

- ↑ Mehra, Jagdish (2000).
*Climbing the mountain: the scientific biography of Julian Schwinger*. Oxford University Press. pp. 1–5. - ↑ "Julian Schwinger Foundation" (PDF).
*nus.edu.sg*. Archived (PDF) from the original on 26 March 2016. Retrieved 1 May 2018. - ↑ Schwinger, J.S.
*Particles, Sources, and Fields.*Vol. 1 (1970) ISBN 9780738200538, Vol. 2 (1973) ISBN 9780738200545, Reading, MA: Addison-Wesley - ↑ Jagdish Mehra, K. A. Milton, Julian Seymour Schwinger (2000), Oxford University Press (ed.),
*Climbing the Mountain: The Scientific Biography of Julian Schwinger*(illustrated ed.), New York: Oxford University Press, p. 550, ISBN 978-0-19-850658-4 CS1 maint: Multiple names: authors list (link), Also Close 1993 , pp. 197–198 - ↑ Brenner, M. P.; Hilgenfeldt, S.; Lohse, D. (2002). "Single-bubble sonoluminescence".
*Reviews of Modern Physics*.**74**(2): 425–484. Bibcode:2002RvMP...74..425B. doi:10.1103/RevModPhys.74.425. - ↑ Schwinger, J. (1982). "Quantum Electrodynamics-An Individual View".
*Le Journal de Physique Colloques*.**43**(C-8): 409. doi:10.1051/jphyscol:1982826. - ↑ Schwinger, J. (1983) "Renormalization Theory of Quantum Electrodynamics: An Individual View", in
*The Birth of Particle Physics*, Cambridge University Press, p. 329. ISBN 0521240050 - ↑ Schwinger, J. (1973). "A report on quantum electrodynamics". In J. Mehra (ed.),
*The Physicist's Conception of Nature.*Dordrecht: Reidel. ISBN 978-94-010-2602-4 - ↑ Beaty, Bill. "Dr. Richard P. Feynman (1918–1988)". amasci.com. Archived from the original on 2007-05-07. Retrieved 2007-05-21.; "A Path to Quantum Electrodynamics," Physics Today, February 1989

- Mehra, Jagdish, and Milton, Kimball A. (2000)
*Climbing the Mountain: the scientific biography of Julian Schwinger*. Oxford University Press. - Milton, Kimball (2007). "Julian Schwinger: Nuclear Physics, the Radiation Laboratory, Renormalized QED, Source Theory, and Beyond".
*Physics in Perspective*.**9**(1): 70–114. arXiv: physics/0610054 . Bibcode:2007PhP.....9...70M. doi:10.1007/s00016-007-0326-6. Revised version published as (2007) "Julian Schwinger: From Nuclear Physics and Quantum Electrodynamics to Source Theory and Beyond,"*Physics in Perspective***9**: 70–114. - Schweber, Silvan S. (1994).
*QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga*. Princeton University Press. ISBN 978-0-691-03327-3. - Ng, Y. Jack, ed. (1996)
*Julian Schwinger: The Physicist, the Teacher, and the Man*. Singapore: World Scientific. ISBN 981-02-2531-8. - Julian Seymour Schwinger (2000), Kimball A. Milton (ed.),
*A quantum legacy: seminal papers of Julian Schwinger*, World Scientific series in 20th century physics,**26**, World Scientific, Bibcode:2000qlsp.book.....K, ISBN 978-981-02-4006-6

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