Elementary Bosons Research Articles

Smatrix of the supersymmetric nonlinearσmodel

We construct the exact $S$ matrix for the supersymmetric nonlinear $\ensuremath{\sigma}$ model in one space and one time dimension. The results confirm that this model possesses mass generation and chiral-symmetry breaking. As a byproduct, we also construct the $S$ matrix for the elementary boson and fermion of the supersymmetric form of the sine-Gordon equation.

Evidence grows for charged heavy lepton at 1.8–2.0 GeV

Early in 1975 Martin Perl and his collaborators at SLAC observed anomalous production of an electron–muon pair in electron–positron annihilation. At the time (PHYSICS TOOAY, October l975, page 17) the group thought they could be observing a heavy lepton, a heavy meson or an elementary boson. By now, the returns from four additional detectors are in. The detector groups reported their results at the International Symposium on Lepton and Photon Interactions at High Energies held in Hamburg late in August. All the groups believe the most likely explanation for the anomalous events is a charged heavy lepton, now called the “tau,” a pointlike particle with mass 1.8–2.0 GeV. The heavy lepton would join its lighter siblings—the electron, muon, electron neutrino and muon neutrino. Presumably the τ would also have its own neutrino. The particle is called τ because it appears to be the third charged lepton to be found, and the Greek word for third begins with τ.

Second-quantized representation for a model system with composite particles

A second-quantized representation for nonrelativistic systems with composite particles is given in which composite particles of two-fermion constituents are described as elementary bosons. The Tani transformation of Girardeau is used to introduce elementary composite fields. An equivalent linear equation of motion method—introducing a ’’d matrix’’—is used in place of the usual nonlinear equation of motion method. This and a diagram formalism are developed to calculate a Hamiltonian and subsidiary condition for this model system and to derive some properties of the Tani transformation.

Gauge hierarchies for chiral SU(N) × SU(N) groups

We have presented a special case where a hierarchy of spontaneous breaking of the symmetries can be achieved in conventional gauge theories (i.e. the Higgs scalars are elementary bosons and the coupling constants of the quartic interactions are small). We break spontaneously the chiral group SU(N) × SU(N) with Higgs scalars transforming like the (N, [Formula: see text]) representation of SU(N) × SU(N). By minimizing the potential we obtain a set of algebraic equations of the type[Formula: see text]where ηj are the vacuum expectation values of the Higgs scalars and μi2 and Aij are parameters. In order to get a hierarchy of spontaneous symmetry breaking we obtain the condition det Aij = 0.

Quantum Field Theory for Bosons with Condensed Phase at a Finite Temperature

A detailed proof is given for the validity of substituting a $c$ number for the zero-momentum-state operators in the quantum-field-theory approach to the many-boson problem at a finite temperature. We use a modification of the method of Kromminga and Bolsterli, and add slightly to their work for the ground-state case. The case in which the bosons which condense are themselves composite particles, as in superconductivity, is treated in this method by the artifice of coupling to a fictitious elementary boson and then letting the coupling become infinitely weak; the self-consistent formulation of Schrieffer for superconductivity can be obtained in this way.

Ground state properties of alpha matter

The ground state of a uniform, extended system of alpha particles at zero temperature is studied by a variational method. The alpha particles are treated as elementary bosons and are assumed to interact through two-body potentials fitting the alpha-alpha elastic scattering data. A cluster development is used to evaluate the expectation value of the energy for a trial ground state wave function of Jastrow form. The conventional Bose cluster expansion is modified to cope with the rather strong angular-momentum dependence of the best phenomenological alpha-alpha potentials. Numerical calculations of the two- and three-body cluster contributions to the energy have been performed over a wide range of densities and variational parameters. Some estimates of the four-body terms have also been made. The convergence of the cluster expansions, for the optimally determined variational parameters, appears quite satisfactory. The resulting equations of state for zero-temperature alpha-matter are of interest in relation to the theory of low-density nuclear matter and, more specifically, the problems of nucleon clustering in the nuclear surface.