Julian Schwinger

Brownian Motion of a Quantum Oscillator

An action principle technique for the direct computation of expectation values is described and illustrated in detail by a special physical example, the effect on an oscillator of another physical system. This simple problem has the advantage of combining immediate physical applicability (e.g., resistive damping or maser amplification of a single electromagnetic cavity mode) with a significant idealization of the complex problems encountered in many‐particle and relativistic fieldtheory. Successive sections contain discussions of the oscillator subjected to external forces, the oscillator loosely coupled to the external system, an improved treatment of this problem and, finally, there is a brief account of a general formulation.

Particles, Sources and Fields

Electrodynamics * Two-Particle Interactions. Non-relativistic Discussion * Two-Particle Interactions. Relativistic Theory I * Two-Particle Interactions. Relativistic Theory II * Photon Propagation Function II * Positronium Muonium * Strong Magnetic Fields * Electron Magnetic Moment * Photon Propagation Function III * Photon Decay of the Pion. A Confrontation.

A Theory of the Fundamental Interactions

This note is an account of some developments in an effort to find a description of the present stock of elementary particles within the framework of the theory of quantized fields’. The theory of fields suggests that the spin values of

Relativistic quantum field theory

5 for F(ermi)-D(irac) fields, and of 0 and 1 for B(ose)-E(instein) fields are not only exceptional in their simplicity but. are likely to be unique in the possibility of constructing a consistent formalism for particles with mass and electric charge. We shall attempt to describe the massive, strongly interacting particles by means of fields with the smallest spin appropriate to the statistics, O(B.E.) and s(F.D.). Spin 1 remains a possibility for B.E. fields but will be assumed to refer to a different family of particles, of which the electromagnetic field may be a special example. If the spin values are thus limited, the origin of the diversity of known particles must be sought in internal degrees of freedom. We suppose that the various intrinsic degrees of freedom are dynamically exhibited by specific interactions, each with its characteristic symmetry properties, and that the final effect of interactions with successively lower symmetry’ is to produce a spectrum of physically distinct particles from initially degenerate states. Thus we attempt to relate the observed masses to the same couplings responsible for the production and interaction of these particles The general multicomponent Hermitian field x separates into the F.D. field J/ and the B.E. field 4. The representation of spin

Coulomb Green's Function

5 requires 4 components, while spin 0 demands 5 components, decomposable into a scalar and a vector. The existence of internal degrees of freedom is expressed by an additional multiplicity

Casimir effect in dielectrics

THE RELATIVISTIC QUANTUM theory of fields was born some 35 years ago through the paternal efforts of Dirac, Heisenberg, Pauli and others. It was a somewhat retarded youngster, however, and first reached adolescence 17 years later, an event which we are gathered here to celebrate. But it is the subsequent development and more mature phase of the subject that I wish to discuss briefly today.THE RELATIVISTIC QUANTUM theory of fields was born some 35 years ago through the paternal efforts of Dirac, Heisenberg, Pauli and others. It was a somewhat retarded youngster, however, and first reached adolescence 17 years later, an event which we are gathered here to celebrate. But it is the subsequent development and more mature phase of the subject that I wish to discuss briefly today.

Casimir self-stress on a perfectly conducting spherical shell☆

A one-parameter integral representation is given for the momentum space Greens function of the nonrelativistic Coulomb problem.

Classical and quantum theory of synergic synchrotron-Čerenkov radiation

We reconsider the Casimir (van der Waals) forces between dielectrics with plane, parallel surfaces for arbitrary temperature, using the methods of source theory. The general results of Lifshitz are confirmed, and are shown to imply the correct forces on metal surfaces. The same phenomena give rise to contributions to the surface tension and the latent heat of an idealized liquid, contributions which, unfortunately, are not well defined since they depend upon a momentum cutoff. However, with a reasonable value for this cutoff, qualitative agreement with the experimentally observed surface tension and latent heat of liquid helium at absolute zero is obtained.

Field theory of unstable particles

Abstract The Casimir stress on a perfectly conducting uncharged sphere, due to occurrence of fluctuations in the electromagnetic field, is calculated using a source theory formulation. Two independent methods are employed: we compute (1) the total Casimir energy inside and outside the sphere, and (2) the radial component of the stress tensor on the surface. It is necessary to exercise care in allowing the field points to overlap; a correct limiting procedure supplies a “cutoff” in the frequency integration. In spite of numerous technical improvements, the result of Boyer, that the self-stress is repulsive (and not attractive as Casimir hoped), is confirmed unambiguously. The magnitude of the Casimir energy of a sphere of radius a is found, by numerical and analytic techniques, to be E = ( h c 2a )(0.09235) , also in agreement with the very recent result of Balian and Duplantier.

Electromagnetic mass revisited

Abstract The power spectra of Cerenkov, synchrotron, and synchrotron-Cerenkov radiation are calculated both classically (by source methods) and quantum mechanically (by mass operator methods). The synergic features of the synchrotron-Cerenkov radiation are pointed out. The existence of a transition region near nβ = 1 [n(ω, H) = index of refraction of the medium; β = v c , v - velocity of the charged particle] coupled with the intrinsic dispersion of the medium is then applied to the discussion of the suppression of X-ray radiation, the construction of X-ray counters, the detection of the quantum corrections, and the modification of the synchrotron radiation from pulsars.