Interatomic forces, phonons, the Foreman-Lomer Theorem and the Blackman Sum Rule

Foreman and Lomer proposed in 1957 a method of estimating the harmonic forces between parallel planes of atoms of primitive cubic crystals by Fourier transforming the squared frequencies of phonons propagating along principal directions. A generalized form of this theorem is derived in this paper and it is shown that it is more appropriate to apply the method to certain combinations of the phonon dispersion relations rather than to individual dispersion relations themselves. Further, it is also shown how the method may be extended to the non-primitive hexagonal close packed and diamond lattices. Explicit, exact and general relations in terms of atomic force constants are found for deviations from the Blackman sum rule which itself is shown to be derived from the generalized Foreman-Lomer theorem.Comment: 13 pages pd

Longitudinal and transverse components of a vector field

A unified account, from a pedagogical perspective, is given of the longitudinal and transverse projective delta functions proposed by Belinfante and of their relation to the Helmholtz theorem for the decomposition of a three-vector field into its longitudinal and transverse components. It is argued that the results are applicable to fields that are time-dependent as well as fields that are time-independent.Comment: 9 pages pdf format. Includes derivation and extension of the Frahm relation and volume integrals of projector

Role of the non-locality of the vector potential in the Aharonov-Bohm effect

When the electromagnetic potentials are expressed in the Coulomb gauge in terms of the electric and magnetic fields rather than the sources responsible for these fields they have a simple form that is non-local i.e. the potentials depend on the fields at every point in space. It is this non-locality of classical electrodynamics that is at first instance responsible for the puzzle associated with the Aharonov-Bohm effect: that its interference pattern is affected by fields in a region of space that the electron beam never enters.Comment: v5. 12 pages, 1 Figure pdf. Two appendices adde

Comparison of different forms for the "spin" and "orbital" components of the angular momentum of light

We compare three attempts that have been made to decompose the angular momentum of the electromagnetic field into components of an "orbital" and "spin" nature. All three expressions are different and it appears, on the basis of classical electrodynamics, that there is no preferred way of decomposing the angular momentum of the electromagnetic field into orbital and spin components, even in an inertial frame.Comment: Some clarifications. 7 pages pdf. Earlier version published in International Journal of Optics: http://www.hindawi.com/journals/ijo/aip/728350

Derivation of the paraxial form of the angular momentum of the electromagnetic field from the general form

It is shown how the standard forms for the spin and orbital components of the angular momentum of a paraxial wave of electromagnetic radiation are obtained from the general expressions for the angular momentum that have been derived recently. This result will enable the general expressions for angular momentum to be applied with confidence to the many configurations of electromagnetic fields that are more complicated than plane or paraxial waves.Comment: typos corrected 6 page

Quantization of the free electromagnetic field implies quantization of its angular momentum

It is shown that when the gauge-invariant Bohr-Rosenfeld commutators of the free electromagnetic field are applied to the expressions for the linear and angular momentum of the electromagnetic field interpreted as operators then, in the absence of electric and magnetic charge densities, these operators satisfy the canonical commutation relations for momentum and angular momentum. This confirms their validity as operators that can be used in quantum mechanical calculations of angular momentum.Comment: 9 pages pdf format. Correct equation (10