Gravitational anomalies

It is shown that in certain parity-violating theories in 4k+2 dimensions, general covariance is spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of $\text{spin}\text{-}\text{1}\text{2}\text{or}\text{-3}\text{2}$ or self-dual antisymmetric tensor fields are coupled to gravity. (For Dirac fermions there is no trouble.) The conditions for anomaly cancellation between fields of different spin is investigated. In six dimensions this occurs in certain theories with a fairly elaborate field content. In ten dimensions there is a unique theory with anomaly cancellation between fields of different spin. It is the chiral n = 2 supergravity theory, which is the low-energy limit of one of the superstring theories. Beyond ten dimensions there is no way to cancel anomalies between fields of different spin.     

Perturbation theory in terms of superfields

A perturbation theory in terms of superfields has been developed for a class of super-symmetric Lagrangians which contain massless spin zero boson and $\text{spin}\text{-}\text{1}\text{2}$ Majorana spinor fields.     

Approaches to the gravitational spin-32 axial anomaly

The $\text{spin}\text{-}\text{3}\text{2}$ axial anomaly is discussed from various points of view. Two consistent theories for a $\text{spin}\text{-}\text{3}\text{2}$ field interacting with gravity are considered: supergravity and a real quantized $\text{spin}\text{-}\text{3}\text{2}$ field in a classical gravitational background. The Feynman graph method, the zeta function regularization method, the point splitting method and the topological method all yield the same result for the latter theory, in agreement with that first found by Christensen and Duff.     

Supersymmetric bound states

We investigate the bound-state spectrum of a supersymmetric version of QED and calculate the energy of the lowest states of the theory to O(α⁴). These states involve a degenerate quartet of $\text{spin}\text{-}\text{1}\text{2}$ and spin-zero states (para-states) and a degenerate quartet of $\text{spin}\text{-}\text{1}\text{2}$ states associated with an additional spin zero and spin one state (ortho-states). Because of the supersymmetry, the ortho-para splitting in positronium is changed from $\text{7}\text{12}\text{mα}{}^4\text{to}\text{1}\text{2}\text{mα}{}^4$.     

Spectrum (super-) symmetries of particles in a Coulomb potential

The Schrödinger equation for a spin-0 particle in the field of a dyon is obtained by dimensional reduction of the four-dimensional harmonic oscillator; the reduction is effected by imposing an equivariance condition on the wave functions of the latter system. This geometrical construction allows for a simple derivation of the SO(4, 2) spectrum symmetry of the dyon system. A supermultiplet of one $\text{spin}\text{-}\text{1}\text{2}$ and two spin-0 particles in a Coulomb potential is demonstrated to possess an N = 2 conformal supersymmetry through a generalization of the same method. The states and wave functions for these systems can be obtained from the representation theory of the corresponding symmetry algebras. A particular case for which this approach provides a complete group theoretical analysis is that of the Pauli equation for a $\text{spin}\text{-}\text{1}\text{2}$ particle in the field of a dyon.     

Gauge internal symmetry in extended supergravity

Extended supergravity theories with global O(2) and SO(3) internal symmetry have recently been constructed, and a mechanism which implements local O(2) and SO(3) gauge invariance is given here. The introduction of a minimal gauge coupling automatically leads to a $\text{spin}\text{-}\text{3}\text{2}$ mass and a cosmological term in order to preserve local supersymmetry. Local internal symmetry for a $\text{spin}\text{-}\text{3}\text{2}$ field is related to spontaneous breakdown of global supersymmetry. Perturbation theory results which confirm the physical consistency of the system are given.     

Ambigous sets of partial-wave amplitudes cannot intersect

The correct set of partial-wave amplitudes can sometimes be distinguished from ambiguous ones because it joins continuously, as a function of energy, to a lower-enegy set known unambiguously. If two sets intersect, however, this continuity criterion yields no unique answer. We show that such an intersection is in fact impossible in the usual experimental spin-0 $\text{spin}\text{-}\text{1}\text{2}$ scattering situation.     

Quantum gravitational bubbles

Spacetime is expected to have a “foamlike” structure on scales of the Planck length or less with high curvatures and complicated topology. This foam can be thought of as being built out of three basic kinds of units or “gravitational bubbles”, CP², S² × S² and K3. We investigate the propagation of particles in simple models of the first two types of bubble. The non-trivial topologies of the bubbles introduce extra singularities into the Green functions. These make large contributions to the S-matrix for scalar particles but only small contributions for $\text{spin}\text{-}\text{1}\text{2}$ or 1 particles at energies small compared to the Planck length. These results suggest that there is no inconsistency between the spacetime foam picture and everyday observations from which spacetime appears nearly flat, because all the elementary particles we have observed have spin $\text{1}\text{2}$ or greater. They do, however, suggest that Higgs scalar fields, if they exist at all, are probably bound states of higher spin particles rather than being elementary fields. Further developments may enable one to calculate processes in which quantum coherence is lost and intrinsic entropy is produced.     

Muon capture by hydrogen and 3He

We present a new calculation of the capture rates, polarizations and asymmetry parameters of the final nucleus in the capture of muons by any $\text{spin}\text{-}\text{1}\text{2}\text{,}\text{isospin}\text{-}\text{1}\text{2}$ nucleus in the non-breakup channel. We treat nuclei as elementary particles and give explicitly the transition amplitude for any spin configuration. We apply our formulae to hydrogen and ³He, obtaining agreement with the experimental data.     

A new representation for the density matrix: (II). Equations of motion

The equations of motion for the new SU(n) parameters representing the density matrix for arbitrary spin are derived. It is shown that for a class of hamiltonians which are diagonal, the equations are exactly solvable by using the device of combining the SU(n) parameters in pairs using the Pauli spin matrix σ_y. It is also shown that using the correspondence relations between the SU(n) parameters and the spherical tensor moments, it is possible to picture the time evolution of the tensor parameters using the explicit solutions for the SU(n) parameters. This procedure has been illustrated by discussing in detail the problem of spin-1 and $\text{spin}\text{-}\text{3}\text{2}$ systems interacting with an external magnetic field and subjected to quadrupole interactions.     

Spin-12 particles in the field of monopoles

The equations of motion of a $\text{spin}\text{-}\text{1}\text{2}$ particle in the field of a point-like (Abelian and non-Abelian) monopole are solved; helicity states and scattering solutions are constructed. The motion in an extended monopole and dyon source is discussed: charge-exchange scattering amplitudes are computed in the distorted-wave Born approximation. By the introduction of suitable spinors, the separation of variables is accomplished for any value of isospin. The non-existence of fermion zero modes in the field of an SU(2) monopole when $\text{T > 1, J >}\text{1}\text{2}$ is shown.     

Index theorem boundary terms for gravitational instantons

We compute the boundary correction terms for the Atiyah-Singer index theorem for spin $\text{1}\text{2}$, 1 and $\text{3}\text{2}$ in asymptotically locally Euclidean (ALE) and asymptotically locally flat (ALF) metrics. In the case of the explicitly known self-dual multi-instanton (ALE) and multi-Taub-NUT (ALF) metrics we find complete agreement with previous work. We also find the corrections to be consistent for an extended class of ALE's which are not explicitly known but which have been constructed implicitly by Hitchin.     

Construction of a unitary analytic amplitude for the scattering of spin-12 particles

We study the existence, the uniqueness and the construction of unitary analytic amplitudes for $\text{spin}\text{1}\text{2}\text{?}\text{1}\text{2}$ scattering, in the framework previously introduced by Atkinson-Mahoux-Ynduráin for spin 0-0, and $\text{spin}\text{0?}\text{1}\text{2}$ scattering.     

Covariant polarization bases for spin=12, 1, 32 particles and their use

A simple method is presented for evaluating transition amplitudes between massive states with $\text{spin}\text{=}\text{1}\text{2}\text{, 1}$ and definite polarization. The $\text{spin}\text{-}\text{3}\text{2}$ case is also briefly discussed. Applications to testing the decay and production of vector bosons are considered.     

On the rigorous determination of the spin-0-spin-12 elastic scattering amplitudes from experimental data and unitarity

The contraction-mapping principle is used to study rigorously the elastic unitarity equations for the scattering of a spin-0 particle by a $\text{spin}\text{-}\text{1}\text{2}$ particle when the unpolarized differential cross section dσ/dΩ and the polarization P at fixed energy below the first inelastic threshold are known from experiment. It is shown that when dσ/dΩ, P and the region where the scattering amplitudes are searched are suitably restricted, the scattering amplitudes exist, are unique and can be found by iterating the unitary equations. Besides, there are other solutions outside that space associated with well-known ambiguities. We show that those ambiguities are solved by measuring the parameters R and A and the sign of the real part of the forward amplitude.     

“Virtual effects of excited quarks as probes of a possible new hardonic mass scale”

The effects of $\text{spin}\text{-}\text{3}\text{2}$ excited quarks are considered as probes of a possible new hadronic mass-scale Λ. A specific model is developed which describes virtual $\text{spin}\text{-}\text{3}\text{2}$ quarks of mass of O(Λ). Induced effects, which are corrections to the standard SU(2) × U(1) electroweak model, include right-handed charged currents and flavor changing neutral currents. A model-independent classification of all SU(3) × SU(2) × U(1) invariant quark operators of dimension six or less is also presented. Ambiguities in converting this analysis and existing experiments to a definitive lower-bound for Λ are discussed. It is found, depending on the strength of certain Higgs couplings and the underlying global flavor symmetries in the absence of Higgs couplings, that a lower bound as small as Λ > 500 GeV or as large as Λ > 100 TeV is possible.     

Supersymmetric flavon-chromon models

Using the supersymmetry and R-breaking mechanism induced by N=1 supergravity, we develop the minimal flavon-chromon preonic model where $\text{spin}\text{-}\text{1}\text{2}$ and spin-0 components of four preonic chiral multiplets correspond to flavons and chromons, from which quarks and leptons are made as composites. The emergence of the concepts of flavour and colour, in this minimal model, is synonymous with R and supersymmetry breaking. This breaking also gives a heavy mass to the gaugino, which is necessary for the implementation of the model.