Search

A Higgs-type symmetry-breaking mechanism with general statistics is described in scalar phi/sup 4/ theories. It is shown that the minimum of the potential depends upon statistics and the parameter space is subdivided into separate regions, each with a particular statistics as a phase variable. In the model we describe, a phase diagram is constructed in parameter space, suggesting a new type of phase transition between domains of different statistics.

An analysis is made of the supersymmetry of parafields in Wess-Zumino-type models with two cases in which parabosons and parafermions form a supermultiplet. In case one the symmetry is realized by either the normal superalgebra or an infinite Lie algebra as in ordinary supersymmetry. In case two the infinite Lie algebra is intrinsic to the supersymmetry. With appropriate symmetry breaking, formulations of these types may be used to explain the generation problem by postulating unobserved parabosons as supersymmetric partners. The relevance to these models of an infinite Lie algebra constructed from supersymmetry is mentioned.

Starting from the standard supersymmetry algebra, an infinite Lie algebra is constructed by introducing commutators of fermionic generators as members of the algebra. From this algebra a finite Lie algebra results for fixed momentum analogous to the Wigner analysis of the Poincare algebra. It is shown that anticommutation of the fermionic charges plays the role of a constraint on the representation. Also, it is suggested that anticommuting parameters can be avoided by using this infinite Lie algebra with fermionic generators modified by a Klein transformation.

A theory is given for the conversion of positrons bound at metal surfaces to free positronium via electron pickup. The method is applied to Al and Ni.

A hidden isospin variable is coupled to the spin of particles observed in an EPR experiment. For spin-1/2 it is shown that isospin i≥3/2 is sufficient to ensure a locally realistic spin distribution. For spin-1, examples of violation of the Mermin-Schwarz inequalities in the case of i=0 are shown satisfied with isospin. The general feature of a softening of quantum nonlocality with isospin is suggested, as well as applications to quantum physics at high energy.

We exhibit generalized parastatistical double commutation relations which allow a solution less restrictive than Green’s ansatz. This leads to local interaction terms in the Lagrangian consistent with an internal symmetry among Green indices. The generalized commutation relations are covariant under this symmetry transformation rather than invariant. The formulation may be applicable to the generation problem as well as supersymmetric model building.

An analysis is made of the characteristics of internal symmetry and symmetry breaking in a quantum field theory with generalized parastatistics, defined by either double commutation relations or single commutation relations. The connection between the two statistics is clarified. We develop a formalism in which statistics is viewed as a dynamical or phase variable of quantum systems. It is shown that the types of Higgs phases possible depend upon statistics. Relationships between physical amplitudes implied by internal symmetry with normal statistics are violated in the case of generalized parastatistics.