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Barely six months after the Shelter Island Conference, which reawakened his interest in quantum electrodynamics (QED), and just three months after returning to Harvard University from his extended honeymoon to the West Coast, Julian Schwinger published a one-page note in the Physical Review entitled ‘On quantum electrodynamics and the magnetic moment of the electron’. A preliminary account of this work was presented by Schwinger at the 10th Washington Conference on Theoretical Physics in November 1947, which attracted the interest of J. Robert Oppenheimer and Richard Feynman. This chapter looks at Schwinger's method of canonical transformations, his covariant approach to QED, Sin-itiro Tomonaga's covariant formulation of quantum field theory, Feynman's theory of positrons and his space-time approach to quantum electrodynamics, Freeman Dyson's research on the radiation theories of Schwinger, Tomonaga, and Feynman, and the synergism between the works of Feynman and Schwinger with respect to QED.

In the beginning of June 1947, the Shelter Island Conference was held in New York to discuss the fundamental problems of quantum mechanics, of which J. Robert Oppenheimer was the acknowledged leader. Schwinger attended the conference upon the invitation of Oppenheimer. After his intensive work on the theory of waveguides at the Massachusetts Institute of Technology's Radiation Laboratory and return to the field of nuclear physics at Harvard University, Schwinger was about to confront the problems of quantum electrodynamics at Shelter Island. This chapter deals with Schwinger's work on quantum electrodynamics, Hans Bethe's calculation of the Lamb shift, Richard Feynman, Schwinger's lecture at the American Physical Society's meeting in New York in 1948 in which he reported his initial results on the Lamb shift and the calculation of the anomalous magnetic moment of the electron, and his participation in the Pocono Conference of 1948.

Prior to 1947, Julian Schwinger had not worked in quantum electrodynamics (QED), apart from his first unpublished paper ‘On the interaction of several electrons’. Before joining the City College of New York, he had already studied Paul Dirac's The principles of quantum mechanics, first published in 1930. As a freshman at CCNY, Schwinger studied the recently published papers on quantum field theory of Dirac, Werner Heisenberg, Wolfgang Pauli, Enrico Fermi, J. Robert Oppenheimer, and others; he absorbed all that was being done in this field. However, he maintained his interest in quantum field theory, and had more exposure to the subject when he went to the University of California at Berkeley to work with Oppenheimer for two years. This chapter deals with Schwinger's work on QED, Dirac's theory of radiation and relativistic theory, relativistic quantum mechanics, the infinities in QED, earlier attempts to overcome the infinities in QED, and earlier experimental evidence for the deviations from Dirac's theory of the electron.

The standard model of non-relativistic quantum electrodynamics describes non-relativistic quantum matter, such as atoms and molecules, coupled to the quantized electromagnetic field. Within this model, this chapter reviews basic notions, results, and techniques in theory radiation. It describes the key technique in this area — the spectral renormalization group. The review is based on joint works with Volker Bach and Jürg Fröhlich and with Walid Abou Salem, Thomas Chen, Jérémy Faupin, and Marcel Griesemer. A brief discussion of related contributions is given at the end of these lectures.

In November 1973 the UCLA Monthly, a periodical for faculty and students of the University of California at Los Angeles (UCLA), published an interview with Julian Schwinger. Since the interview reveals many of Schwinger's views about science and society, which he seldom shared with the public, this final chapter begins by quoting the interview, conducted by Mark Davidson. Among the topics he addressed were whether he thinks scientists are sufficiently concerned about the moral implications of their work, Albert Einstein's contention that man's way of thinking must change, whether scientists he met in various countries tend to think like citizens of the world, and his reputation as a public crusader. This chapter also looks at Schwinger's interest in music and composition, sports, reading, cats, and travel. Schwinger's tributes to fellow physicists Sin-itiro Tomonaga, who died in 1979, and Richard Feynman, who died in 1988, are also presented. Tomonaga and Feynman were his co-recipients of the Nobel Prize for Physics in 1965 for their formulation of renormalised quantum electrodynamics.

Julian Schwinger had now scaled the peak of quantum electrodynamics (QED), not once, but three times, the last time by inventing a new approach to any quantum-mechanical system, the quantum dynamical principle. Now the task of the field theorist, as was already apparent in the 1930s, was to build upon this success of QED and apply the powerful machinery invented to understand the strong and weak nuclear interactions. This chapter describes the story of Schwinger's work in the central period between the quantum field theory revolutions of the late 1940s and the early 1970s, roughly during the period 1957 through 1965. Schwinger's work on the phenomenological field theory, dispersion relations, spin and the TCP theorem, Euclidean field theory, gauge invariance and mass, quantum gravity, and magnetic charge are examined.

As soon as Julian Schwinger burst upon the stage, one could hardly doubt that a Nobel Prize was in the offing. Certainly, after his solution of the problems of quantum electrodynamics in the late 1940s the award of the Nobel Prize was just a matter of time. Yet years passed with no news of the award. Clarice Schwinger, his devoted wife, described waiting for the Prize and thought he would get it soon after they got married. When it did not happen, she then decided Julian simply was not going to get it. This chapter looks at Schwinger's winning the Nobel Prize for Physics in 1965 and the attention he received afterwards, his Nobel lecture entitled ‘Relativistic quantum field theory’ delivered in December 1965, his development of the source theory as an alternative to the operator quantum field theory, source theory calculation of the anomalous magnetic moment of the electron, Schwinger's research on chiral symmetry, his influence on Steven Weinberg with regards to effective Lagrangians, and his last years as a professor at Harvard University.

In quantum electrodynamics, the matter degrees of freedom are coupled to the radiation field through a local, gauge-invariant interaction density. Due to the linear structure of this coupling, the problem of constructing a complete formal representation of the reduced matter dynamics can be solved exactly if the electromagnetic radiation field is initially in a Gaussian state. This chapter combines field theoretical methods with superoperator and influence functional techniques to derive an exact, relativistic representation for the reduced density matrix of the matter degrees of freedom which completely describes the influence of the electromagnetic radiation field on the matter dynamics. Several applications are treated, such as the suppression of the quantum coherence of charged particles caused by the emission of bremsstrahlung and the decoherence of many-particle states.

“We do not really know what energy is”. This was the conclusion of Richard Feynman, who in the 20th century contributed so much to our understanding of the nature of energy. The first chapter deals in particular with its role in establishing the expression “elementary particle” – or what in various phases of our growing knowledge was so termed. Theory and experiment are described with equal emphasis. Theory includes Einstein’s special and general relativity, the two approaches to quantum mechanics by Heisenberg and Schrödinger, as well as some fundamental expansions of the theory in the second half of the 20th century, including the quantum electrodynamics “created” by Sin-Itiro Tomonaga, Julian Schwinger, Richard Feynman and Freeman Dyson, and quantum chromodynamics, a brain-child of (in particular) Murray Gell-Mann. Other new insights, up to the standard model of particle physics, are mentioned here. Some are described in depth, though without mathematical detail. Experiments that have led to fundamentally important results are described in balance with theory. All this is discussed in the context of the title of the book. A comparison with living systems shows that animate matter needs to have more complex properties than do the “strangely simple” building-blocks of inanimate matter.

This chapter highlights major breakthroughs in the history of quantum field theory. It focuses on studies which had a definitive impact in, firstly, the development of the formal structure of quantum field theory; and, secondly, uncovering and (partially) resolving the conceptual difficulties occasioned by the lack of explicit relativistic covariance and by the appearance of ultraviolet divergencies in early calculations of quantum electrodynamic processes. The theories of Dirac, Jordan, Klein, Wigner, Pauli, and Heisenberg are discussed.

This chapter begins with a discussion of the two important papers Pauli wrote with Heisenberg. The activity was stimulated by Dirac who on 2 February 1927 submitted his first paper on quantum electrodynamics. It details Pauli’s arrival in Zurich as a new professor in 1928, his marriage to Kate Deppner in 1929, and the discovery of the neutrino.

This chapter illustrates the regularization of field theory by taking quantum electrodynamics (QED) as an example, showing that the mass of the photon remains at 0 even after higher-order quantum corrections. The simplest example of the quantum breaking of chiral symmetry is also explained. The one-loop fermionic diagrams become fundamental in these considerations, and the gauge covariant regularization of one-loop Feynman diagrams for arbitrary theory is explained. It is shown that the chiral anomaly is defined independently of Feynman diagrams in perturbation theory. The basic idea of the Adler-Bardeen theorem, which asserts that identity with the chiral anomaly does not receive any higher-order corrections, is briefly discussed.

In connection with the cavity quantum electrodynamics, this chapter reviews the optical properties of a few mode semiconductor microcavity with embedded quantum dots. Both the weak (Purcell effect) and strong (polariton effect) coupling limits of microcavity single-mode light ‘quantum dot’ interaction are discussed. The experimental realization of the strong coupling limit is illustrated for a high-quality (high-Q) GaAs-based pillar microcavity.

The modern theory of particle physics, called the Standard Model, describes electromagnetic, weak, and strong forces and all known forms of matter in terms a single conceptual principle. This chapter gives a short overview of the events that led to the discovery of this theory. It first explains the meaning of quantum field theory, which is the language used to describe the particle world. It then presents QED, the theory which describes the electromagnetic phenomena in the domain of particle physics. Finally, the Standard Model emerges from the synthesis of three intertwined stories: the discovery of quarks, the unification of electromagnetism with the weak force, and the understanding of the strong force in terms of QCD.

This chapter describes two cavity quantum electrodynamics (CQED) studies guided by the spirit of thought experiments. The first one is a direct implementation of the recoiling slit interferometer imagined by Bohr. Section 6.1 discusses a closely related experiment, in which a Ramsey interferometer is used instead of the unrealistic Young's one proposed by Bohr. The second experiment, described in Section 6.2, realizes another dream of early quantum mechanics by achieving a non-destructive detection of a single photon. Section 6.3 shows that the quantum non-demolition (QND) measurement of a single photon by a Rydberg atom corresponds to the operation of a control-not quantum gate in which the photon is the control bit and the atom the target. Section 6.4 discusses the extension of the atom-field manipulations to larger fields, based on the dispersive atom-cavity interaction. Section 6.5 describes an alternative statistical method, also based on the atom-field dispersive interaction. The method relies on the preliminary translation of the field in phase space by controlled complex amplitudes.

This chapter is devoted to the physics of cavity quantum electrodynamics (CQED) cats. After a brief reminder about the Schrödinger cat problem in quantum optics, it describes how a single atom interacting with a field made of many photons can leave its quantum imprint on this field, bringing it into a superposition of states with distinct classical attributes. It describes the preparation and detection of these ‘Schrödinger cat’ states. It presents simple decoherence models, which account for their extreme fragility. It describes experimental studies of decoherence, which constitute direct explorations of the quantum-classical boundary. It discusses limitations to the size of these cat states and ways to protect them efficiently against decoherence. Finally, the chapter describes proposals to generate and study non-local cats, superpositions of field states delocalised in two cavities.

This chapter focuses on the impact of field quantization methods on the problem of quantum gravity. It is shown that much work after 1930 until mid-century was an exercise in ‘exploring the consequences’ of the Heisenberg-Pauli theory of quantum electrodynamics: understanding the symmetries and the divergences, and attempting to find ways of dealing with both. The goal was very much to treat all fields in much the same way, and so one could also envisage learning about one field from another. However, there was a separate track, superficially similar, though issuing from a desire to have a theory of gravitation more in line with the rest of physics, and in particular one not involving the difficulties of curved, dynamical spacetime. The interaction representation and a desire for a manifestly covariant description played a crucial role in the development of such approaches, and involved a curious borrowing of concepts often associated with canonical approaches. An apparently orthogonal approach developed alongside these later manifestly covariant approaches, involving a hybrid approach retaining a classical gravitational field, albeit still coupled to quantized sources through the Einstein field equations. These were done largely to avoid complications, however, and the conceptual consequences, though hinted at, were not further explored.

This chapter discusses the experimental methods developed in the field of cavity quantum electrodynamics (CQED). Section 5.1 presents a short history of CQED. Section 5.2 describes the circular Rydberg atoms and the superconducting cavities that are the two ‘partners’ in these experiments, and analyses the coupling between them. As first examples, Section 5.3 presents two basic experiments unveiling in a dramatic way the quantumness of the atom-field system. Section 5.4 describes entanglement procedures in CQED, showing how the resonant Rabi oscillation is used to entangle one atom and the field, two atoms, or two field modes. The chapter concludes by describing non-resonant atom-cavity experiments that provide an alternative recipe for atom-atom entanglement.