Ranging from the physics of elementary particles to the structure of viruses, the subject matter of this book stresses the importance of optical activity and chirality in modern science and will be of interest to a wide range of scientists. Using classical and quantum methods with a strong emphasis on symmetry principles, the volume develops the theory of varied optical activity and related phenomena from the perspective of molecular scattering of polarized light. First Edition Hb (1983): 0-521-24602-4

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Molecular Light Scattering and Optical Activity

http://cds.cern.ch/record/503806/files/0106045.pdf

New developments in the Casimir effect

Maxwell’s equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect—surface modes with strong spin-momentum locking. These modes are evanescent waves that form, for example, surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments that have demonstrated the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell’s theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces.

http://science.sciencemag.org/content/sci/348/6242/1448.full.pdf

Quantum spin Hall effect of light

Momentum and spin represent fundamental dynamic properties of quantum particles and fields. In particular, propagating optical waves (photons) carry momentum and longitudinal spin determined by the wave vector and circular polarization, respectively. Here we show that exactly the opposite can be the case for evanescent optical waves. A single evanescent wave possesses a spin component, which is independent of the polarization and is orthogonal to the wave vector. Furthermore, such a wave carries a momentum component, which is determined by the circular polarization and is also orthogonal to the wave vector. We show that these extraordinary properties reveal a fundamental Belinfante's spin momentum, known in field theory and unobservable in propagating fields. We demonstrate that the transverse momentum and spin push and twist a probe Mie particle in an evanescent field. This allows the observation of 'impossible' properties of light and of a fundamental field-theory quantity, which was previously considered as 'virtual'.

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Extraordinary momentum and spin in evanescent waves

We develop a theoretical model that explains the formation of hot coronae around strongly magnetized neutron stars—magnetars. The starquakes of a magnetar shear its external magnetic field, which becomes nonpotential and threaded by an electric current. Once twisted, the magnetosphere cannot untwist immediately because of its self-induction. The self-induction electric field lifts particles from the stellar surface, accelerates them, and initiates avalanches of pair creation in the magnetosphere. The created plasma corona maintains the electric current demanded by ∇ × and regulates the self-induction EMF by screening. This corona persists in dynamic equilibrium: it is continually lost to the stellar surface on the light crossing time ~10-4 s and replenished with new particles. In essence, the twisted magnetosphere acts as an accelerator that converts the toroidal field energy to particle kinetic energy. Using a direct numerical experiment, we show that the corona self-organizes quickly (on a millisecond timescale) into a quasi-steady state, with voltage 108-109 V along the magnetic lines. The voltage is maintained near the threshold for e± discharge. The heating rate of the corona is ~1036 ergs s-1, in agreement with the observed persistent, high-energy output of magnetars. We deduce that a static twist that is suddenly implanted into the magnetosphere will decay on a timescale of 1-10 yr. The particles accelerated in the corona impact the solid crust, knock out protons, and regulate the column density of the hydrostatic atmosphere of the star. The transition layer between the atmosphere and corona may be hot enough to create additional e± pairs. This layer can be the source of the observed 100 keV emission from magnetars. The corona emits curvature radiation and can supply the observed IR-optical luminosity.

https://iopscience.iop.org/article/10.1086/508917/pdf

Corona of Magnetars

This chapter reviews the electrodynamics of hadrons. Hadrons take part in strong interactions. Hadrons include protons and neutrons with spin 1/2, pions with spin 0, and other particles. Atomic nuclei, which consist of protons and neutrons, are also hadrons. It is impossible to set up equations that determine the electromagnetic interactions of hadrons without taking account of the powerful strong interactions. The hadron current is a phenomenological quantity whose structure is determined by the general kinematic requirements, independent of any assumption about the dynamics of the interactions. If the charged hadron has spin 1/2, the calculations are unchanged; only the specific form of the vertices and propagators is altered. In the limit of low frequencies, the cross section for the scattering of a photon by any charged particle at rest tends to its classical value given by Thomson's formula.

Electrodynamics of hadrons

This chapter describes asymptotic formulae of quantum electrodynamics. The asymptotic constancy of the total cross-section is a characteristic property of scattering processes whose diagrams can be cut across internal photon lines. It occurs even when more than two particles are present in the final state of the reaction. The double-logarithmic corrections occur in cases of two kinds. One kind includes scattering through a fixed finite angle. The cross-sections decrease in the asymptotic high-energy range. In such cases, the double-logarithmic corrections are associated with the infrared divergence. These cases include elastic scattering of electrons in an external Coulomb field. The other class of cases includes reaction cross-sections, which decrease with increasing energy for a given square of the momentum transfer, that is, for scattering angles, which asymptotically approach zero or π.

Asymptotic formulae of quantum electrodynamics

Elastic scattering of an electron in a constant external field is a simple process, which occurs even in the first approximation of perturbation theory. In the nonrelativistic case, the bispinor amplitudes of the plane waves reduce to the nonrelativistic amplitudes. This chapter explores the interaction of electrons. In classical electrodynamics, a system of interacting particles can be described by means of a Lagrangian function depending on the coordinates and velocities of the particles. In the quantum theory, this corresponds to the possibility of describing the system by Schrodinger's equation including second-order terms. However, the usual quantum-mechanical calculation of these forces is inapplicable at large distances, because this calculation considered only the electrostatic interaction, that is, the retardation effects are ignored.

Interaction of electrons

Publisher Summary
The radiative corrections arise from the interaction between the photon field and the electron–positron field. The interaction of the photon with the electron vacuum can be shown by associating the internal closed loops in the photon self-energy diagrams with the electrons. The photon interacts with the fields of other particles; the interaction with the vacua of these fields is described by similar self-energy diagrams, in which the internal loops are associated with the appropriate particles. The particles whose mass is closest to that of the electron are the muons and the pions. For muons, the radiative corrections can be calculated by means of the existing theory, but for pions, they cannot. This places a fundamental limitation on exact calculations of specific effects in present-day quantum electrodynamics. The use of arbitrarily high-order corrections from the photon–electron interaction would be an invalid exaggeration of the attainable accuracy. The method of direct regularization of the Feynman integrals might be demonstrated by a calculation of the mass operator. The radiative corrections cause a shift of the energy levels of bound states of an electron in an external field, called the Lamb shift.

Chapter xii – radiative corrections

This chapter discusses the interaction of electrons with photons. It presents the calculation of the cross section for the scattering of polarized photons by an unpolarized electron, summed over polarizations of the final electron. The cross section for scattering of unpolarized photons with detection of a polarized photon has similar properties. It has been shown that the qualitative properties of the polarization effects in the scattering of photons by electrons follow from the general requirements of symmetry. A pseudoscalar cannot be formed from two polar vectors. The parameters of linear polarization are related to the components of the two-dimensional symmetric tensor. Reaction channels differing by an interchange of initial and final photons correspond to the same process—scattering of a photon by an electron. The squared modulus of the amplitude and the scattering cross section must be invariant under a transformation that expresses the change from one of these channels to the other. Owing to the conservation of momentum, the annihilation of the electron and positron in positronium must be accompanied by the emission of at least two photons. The main process determining the lifetime of positronium is two-photon annihilation for parapositronium and three-photon annihilation for orthopositronium. The decay probability can be related to the cross section for annihilation of a free pair.

E.M. Lifshitz

Papers

Electrodynamics of hadrons

Asymptotic formulae of quantum electrodynamics

Interaction of electrons

Chapter xii – radiative corrections

Interaction of electrons with photons