Supersymmetry and the division algebras

We show how spinors in space-times of dimension D = t + s, where t is the time dimension, are associated for s - t = 1, 2, 4, 8 (and if t = 0, 1, 2) with the number systems (division algebras), $\text{|R, C, H, O}$. For t = 1 and s - t = 1, 2, 4 this association is “realized” by the sequence of Lorentz groups S1(2,$\text{|R}$), S1(2;$\text{|C}$), S1(2;$\text{|H}$) for D = 3, 4, 6 respectively. We discuss how octonions may be related to D = 10. For D = 6 we give details of S1(2; $\text{|H}$) spinors and construct supersymmetric models with them. These results explain various “empirical” observations in the literature relating quaternions and supersymmetry.     

The relaxed hypermultiplet: An unconstrained N = 2 superfield theory

We present an off-shell version of the hypermultiplet, without a central charge or gauge antisymmetric tensors. We give the unconstrained superfield form of the action and its coupling to N = 2 super-Yang-Mills theory. This allows an N = 2 superspace formulation of the N = 4 super-Yang-Mills theory, whose ultraviolet finiteness is then ensured by N = 2 non-renormalization theorems.     

Antisymmetric tensor gauge theories and non-linear σ-models

Antisymmetric tensor fields B_μν subject to the gauge transformation δB_μν = ?_μξ_ν ? ?_νξ_μ can describe spinless particles. We investigate the properties of field theories with a “non-abelian generalization” of this invariance. One class of such theories is equivalent to non-linear principal chiral σ-models, another to massive Yang-Mills theories. A supersymmetric analogue in 2 + 2 superspace is constructed and leads to the supersymmetric σ-model defined on a general riemannian manifold.     

Simplified Bethe-Salpeter equation for positronium

The Bethe-Salpeter equation for a fermion-antifermion system, coupled by photons, is considered in the Feynman gauge. The kernel is that resulting from exchange of a single photon. The usual reduction of the sixteen B-S spinor amplitudes in terms of tensors leads to 16 coupled integro-differential equations. By straightforward application of charge conjugation-, parity-, and Lorentz-invariance, the system of coupled equations is reduced to ones involving no more than eight and as few as three scalar structure functions for the various parity, charge conjugation, and total angular momentum states. The results hold for arbitrary coupling strength. As a check of the equations obtained, a perturbation theory is carried out for the Coulomb interaction. It leads to effective potentials in agreement with those obtained previously to order mα⁴ for positronium.     

Ferrimagnetic transition in Fe0.9S: Magnetic,thermodynamic and kinetic aspects

Antiferromagnetic Fe_0.9S forms a ferrimagnetic superlattice in a narrow temperature range centred at 475 K (γ-transition). We have made a study in single crystals by specific heat, Mössbauer spectroscopy and magnetic susceptibility of the magnetic structure and kinetics and thermodynamics of formation of the ferrimagnetic component.The antiferromagnetic alignment and the spontaneous moment lie in the c-plane. The magnetic anisotropy energy is of the order of 0.4 K per Fe ion. Above 475 K and below T_N ≈ 598 K there is a change in ordering of the vacancies and a new antiferromagnetic structure is formed. At lower temperatures our value (100 kJ mol^?1) of the activation energy of diffusion of iron vacancies, determined from magnetic susceptibility, is in quite good agreement with the value (88 kJ mol^?1) obtained from radiotracer measurements by Condit et al.     

Vanishing β-functions in extended supergravities

Given that extended supergravity theories can be written in N = 1 superfield form, the non-renormalization of chiral superspace integrals implies a vanishing β-function for the SO(N) gauged Poincaré supergravity theories for N ? 5 at one loop and probably to all orders. In particular, this explains the results of existing one-loop calculations of the β-function.     

Magnetic susceptibility of single-crystal hexagonal nickel sulphide

The magnetic susceptibilities of five single-crystals of hexagonal NiS, with compositions ranging from NiS-NiS_1.02 have been measured in the temperature range 78–300°K. The susceptibility curves have a markedly different shape from that normally predicted for an antiferromagnet. This results from the first-order character of the phase transition at T_N.     

Reactions of O 3PJ atoms with halogens: The rate constants for the elementary reactions O + BrCl,O + Br2, and O + Cl2

Direct determinations of the rate constants (cm³/molec · sec) k₁, k₂, and k₃ from 298 to 299°K are reported, using atomic resonance fluorescence in discharge flow systems:

1 One standard deviation.

The rate constant k₁, which has not been determined previously, was found to possess an insignificant temperature coefficient (E_A = (0 ± 700) J/mole) in the range of 299 to 619°K. The present result for k₂ agrees well with reinterpreted values from the one previous determination. Measurements of O atom consumption rates and Br atom production rates in the O + Br₂ reaction are interpreted to give an estimate of the rate constant k₄, which has not been reported previously, at 298°K: k₃ has been measured at three temperatures between 299 and 602°K. The present and previous results for k₃ were combined to give the following rate expression: