Localised configurations of the free electromagnetic field are constructed, possessing properties of massive, spinning, relativistic particles. In an inertial frame, each configuration travels in a straight line at constant speed, less than the speed of lightc, while slowly spreading. It eventually decays into pulses of radiation travelling at speedc. Each configuration has a definite rest mass and internal angular momentum, or spin. Each can be of “electric” or “magnetic” type, according as the radial component of the magnetic or electric field (...) vanishes in the rest frame, and each has an “antiparticle.” Any such configuration, of electric or magnetic type, is characterized in part by a set of labels (κ, ω0, σ,l, m), where ω0 is the mean of the angular frequencies of the plane waves making up the configuration, σ is the variance of those frequencies, κ is a positive constant with dimensions of action, andl, m are angular momentum “quantum numbers” withl a positive integer andm an integer such that ‖m‖≤l. The rest energy of the “particle” is κω0, its spin is κ ‖m‖, and its lifetime is of the order of 1/σ. Its antiparticle has ω0 replaced by −ω0. (shrink)

Compact quantum systems have underlying compact kinematical Lie algebras, in contrast to familiar noncompact quantum systems built on the Weyl-Heisenberg algebra. Pauli asked in the latter case: to what extent does knowledge of the probability distributions in coordinate and momentum space determine the state vector? The analogous question for compact quantum systems is raised, and some preliminary results are obtained.

The phenomenon of probability backflow, previously quantified for a free nonrelativistic particle, is considered for a free particle obeying Dirac's equation. It is shown that probability backflow can occur in the opposite direction to the momentum; that is to say, there exist positive-energy states in which the particle certainly has a positive momentum in a given direction, but for which the component of the probability flux vector in that direction is negative. It is shown that the maximum possible amount of (...) probability that can flow “backwards,” over a given time interval of duration T, depends on the dimensionless parameter ε = (4ℏ/mc2T)1/2, where m is the mass of the particle and c is the speed of light. At ε = 0, the nonrelativistic value of approximately 0.039 for this maximum is recovered. Numerical studies suggest that the maximum decreases monotonically as ε increases from 0, and show that it depends on the size of m, ℏ, and T, unlike the nonrelativistic case. (shrink)

Schwinger’s algebra of microscopic measurement, with the associated complex field of transformation functions, is shown to provide the foundation for a discrete quantum phase space of known type, equipped with a Wigner function and a star product. Discrete position and momentum variables label points in the phase space, each taking \(N\) distinct values, where \(N\) is any chosen prime number. Because of the direct physical interpretation of the measurement symbols, the phase space structure is thereby related to definite experimental configurations.