A relatively simple semiempirical method is suggested for calculating interatomic potentials of ground and low-lying excited states of diatomic systems composed of an alkali atom and a ground-state noble-gas atom, and its applicability to other systems is discussed. Two types of interaction are included: an electrostatic interaction which yields the asymptotic R−6 behavior characteristic of van der Waals potentials, and a pseudointeraction which represents the effect of the Pauli exclusion principle on overlapping electron states. For the electrostatic interaction, the noble-gas atom is treated as a polarizable dipole with two parameters, namely a polarizability α and a “radius” r0. The value of r0 is chosen by adjusting the depth of the ground-state well to agree with recent scattering data. To determine the interatomic potentials, the total Hamiltonian including spin–orbit coupling is diagonalized in a limited basis set of atomic orbitals. Results are presented and compared with previous calculations and experiments.

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We extend a procedure for construction of the photon position operators with transverse eigenvectors and commuting components [Phys. Rev. A 59, 954 (1999)] to body rotations described by three Euler angles. The axial angle can be made a function of the two polar angles, and different choices of the functional dependence are analogous to different gauges of a magnetic field. Symmetries broken by a choice of gauge are re-established by transformations within the gauge group. The approach allows several previous proposals to be related. Because of the coupling of the photon momentum and spin, our position operator, like that proposed by Pryce, is a matrix that does not commute with the spin operator. Unlike the Pryce operator, however, our operator has commuting components, but the commutators of these components with the total angular momentum require an extra term to rotate the matrices for each vector component around the momentum direction. Several proofs of the nonexistence of a photon position operator with commuting components are based on overly restrictive premises that do not apply here

Lecture 1: Introduction to Clifford Algebras Pertti Lounesto 1.1 Introduction • 1.2 Clifford algebra of the Euclidean plane • 1.3 Quaternions • 1.4 Clifford algebra of the Euclidean space 3 • 1.5 The electron spin in a magnetic field • 1.6 From column spinors to spinor operators • 1.7 In 4D: Clifford algebra Cℓ 4 of 4 • 1.8 Clifford algebra of Minkowski spacetime • 1.9 The exterior algebra and contractions • 1.10 The Grassmann-Cayley algebra and shuffle products • 1.11 Alternative definitions of the Clifford algebra • 1.12 References Lecture 2: Mathematical Structure of Clifford Algebras Ian Porteous 2.1 Clifford algebras • 2.2 Conjugation • 2.3 References Lecture 3: Clifford Analysis John Ryan 3.1 Introduction • 3.2 Foundations of Clifford analysis • 3.3 Other types of Clifford holomorphic functions • 3.4 The equation D k ƒ = 0 • 3.5 Conformal groups and Clifford analysis • 3.6 Conformally flat spin manifolds • 3.7 Boundary behavior and Hardy spaces • 3.8 More on Clifford analysis on the sphere • 3.9 The Fourier transform and Clifford analysis • 3.10 Complex Clifford analysis • 3.11 References Lecture 4: Applications of Clifford Algebras in Physics William E. Baylis 4.

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