Sum rules based on current algebra are obtained for the currents evaluated between states of arbitrary spin and mass. Both the infinite-momentum limit and the dispersion method are shown to yield the same result. These sum rules are given explicitly for the crossed-channel amplitudes. © 1967 The American Physical Society.

With a complex arrangement of magnetic fields and magnetic couplings, electrons governed by a standard tight-binding Hamiltonian on a square lattice can be made to obey a Dirac equation with an unequal number of positive and negative masses. This induces a spontaneous quantized Hall conductance. © 1989.

The structure constants appearing in the Poisson-brackets relations among constraints in the Hamiltonian theory of gravity depend on the properties of deformations of a d-dimensional spatial manifold embedded in a (d+1)-dimensional continuum. The study of such deformations is extended to the case where the d-dimensional manifold is a piecewise flat Regge lattice. Although we cannot say whether the algebra of deformations does or does not close for the general lattice, should it close we provide a prescription for obtaining the structure constants. We discuss the case of small lattices where closure can be demonstrated explicitly. © 1987 The American Physical Society.

It is shown that a lattice gauge theory based on the group G is equivalent to a lattice spin theory invariant under a global group which is an infinite direct product of G's. A method of inducing a lattice gauge theory is presented. © 1983.

A scaling relation, dln[σn(s)]dlns→p(nlns), for high-energy production of n particles is proposed. This relation is supposed to be valid for large n and large s. An extension to present energies is suggested and compared with experiment. © 1973 The American Physical Society.

Five dimensional gravity coupled, both in the bulk and on a brane, to a scalar Liouville field yields a geometry confined to a strip around the brane and with time dependent scale factors for the four geometry. In various limits known models can be recovered as well as a temporally expanding four geometry with a warp factor falling exponentially away from the brane. The effective theory on the brane has a time dependent Planck mass and “cosmological constant.” Although the scale factor expands, the expansion is not an acceleration. © 2004 The American Physical Society.

Instabilities of two dimensional (1+1) de Sitter space induced by interacting fields are studied. As for the case of flat Minkowski space, several interacting fermion models can be translated into free boson ones and vice versa. It is found that interacting fermion theories do not lead to any instabilities, while the interacting bosonic sine-Gordon model does lead to a breakdown of de Sitter symmetry and to the vanishing of the vacuum expectation value of the S matrix. © 2010 The American Physical Society.

With certain assumptions on the coupling of two currents to particles of increasing spin, it is shown that the Van Hove model results in Bjorken scaling and Regge asymptotic behavior. The fields corresponding to these particles are related to the products appearing in the operator-product expansion near the light cone. © 1971 The American Physical Society.

A discrete version of a moving-frame formalism is developed and is used to obtain lattice gravity in a Hamiltonian formulation. It is more straightforward to transcribe the constraints of these theories from the continuum to the lattice using these techniques rather than the ordinary Regge calculus. The closure of the algebra of constraints has not been studied. © 1988 The American Physical Society.

A WKB approximation to the Hartree equations for an atom, taking the 1 r singularity of the potential into account, is developed. This in turn allows us to obtain in a systematic way the Z -1 3 and Z -2 3 corrections to the Thomas-Fermi model of the atom. Such a procedure is used to obtain a finite change density at the nucleus, which agrees well with Hartree-Fock values. © 1982.