I show that spin-spin contact interactions occur in a quantum version of Einstein's conventional theory, which are of the same order of magnitude as those occurring in Einstein-Cartan-Sciama-Kibble (ECSK) theory. Thus, all the features which were thought to be peculiar to the ECSK theory—singularity behavior, possibility of stopping gravitational collapse, and so on—actually occur in Einstein's theory. In addition, I examine a contact term (independent of spin orientations and analogous to the Darwin term of quantum electrodynamics) which always gives rise to repulsive gravitation forces.

The Lax equation of nonlinear wave theory is described in a purely Lie-algebraic context. A realization—independent of linear operator theory—which leads to the Kortewegde Vries equation is described in terms of the Poisson-Moyal Lie algebra of quantum mechanics. This approach leads to a generalization of the Euler rigid-body equations.

A measure of the "dependency" of a many-particle system is defined and its time dependence is evaluated for systems initially described by a single Slater determinant. An uncertainty product between the energy spread of the initial determinant and the lifetime of a system's independence is established. Numerical estimates of some lifetimes are given. They are not so long as to be reassuring for nuclear time-dependent Hartree-Fock calculations. Each separate case ought to be checked.

Evidence is given for the existence of a heretofore undetected low-density critical point in a classical fluid of charged hard spheres.

The path integral of quantum gravity probes space-times with nontrivial topology and induces chiral symmetry breaking via an anomaly proportional to ${\epsilon }^{\mu \nu \rho \sigma }R_{}^{\alpha }{}_{\beta \mu \nu }{}^{}R_{}^{\beta }{}_{\alpha \rho \sigma }{}^{}$ in the divergence of the axial fermion number current. The corresponding classical instanton solution of Einstein's equations with cosmological term is found. The Euler-Poincaré characteristic and ordinary instanton number are also discussed.

A renormalization-group method is developed to study critical phenomena in a disordered system. The method bases its considerations on a generalized probability distribution which incorporates both thermodynamic and configurational averaging. Special attention is paid to the higher-order critical phenomena that occur at the percolation limit. A crossover scaling theory describes this region. The equation of the critical line is obtained for the Ising model.

Recently I argued that Yang's pure-space equations must be supplemented by restrictions on the class of allowable space-times. I now consider time-dependent solutions of the pure-space equations and prove the violation of Birkhoff's theorem. Time-dependent spherically symmetric solutions are displayed, as well as solutions representing plane gravitational waves. The suggestion is made that pure spaces are unphysical and Yang's theory requires the explicit presence of a source in vacuum, in contrast to general relativity.

We report measurements of changes in the dielectric constant $\epsilon$ of ${\mathrm{SF}}_6$ along a near critical isochore. We find an anomalous increase in $\epsilon$. The amplitude of the anomaly is about 10 times larger than the one predicted by current theories, which assume a constant polarizability.

It is shown that a region containing closed timelike lines cannot evolve from regular initial data in a singularity-free asymptotically flat space-time. Furthermore, the causality assumption made in the black-hole uniqueness proofs is justified: It is demonstrated that no physically realistic nonsingular black hole can have a causality-violating exterior.

It is shown that an appropriately defined magnetization has a zero thermal average above a critical temperature and a nonzero average below it for a specific lattice Hamiltonian with three-spin interactions in two or more dimensions. This work implies the existence of a phase transition in Reggeon field theory.

Renormalization group ideas are applied to the problem of first-order phase transitions in Ising-like models. They support the existence of essential singularities as the coexistence region is approached, at all temperatures below the critical temperature.

Lattice-gas phase boundaries have been calculated for the simple quadratic and honey-comb lattices from the corresponding antiferromagnetic critical curves. Results were obtained using nonlinear renormalization group methods with periodic cell clusters. The result for the simple quadratic lattice is in excellent agreement with the existing temperature-series result.

The ($H_x, H_y, H_z$) phase diagram of a cubic ferromagnet with three easy axes, in a field $\overrightarrow{\mathrm{H}}=(H_x, H_y, H_z)$, is studied by mean-field, scaling, and renormalization-group theories. For $T<\mathrm{}{T}_c\mathrm{}(H=0\mathrm{})\mathrm{}$ and $\overrightarrow{\mathrm{H}}\parallel \mathrm{}\left[111\right]\mathrm{}$ there is a phase transition at fields $\pm H_0\mathrm{}\left(T\right)\mathrm{}$, described by the three-component Potts model. By varying $\overrightarrow{\mathrm{H}}$ the full phase diagram of the three-dimensional Potts model is experimentally accessible and competing predictions of the multicritical behavior can be tested.

For all complex space-times in which the self-dual part of the Weyl tensor is algebraically degenerate, Einstein's vacuum equations are reduced to a single differential equation of the second order and second degree.

I discuss the basic ideas in applying the Monte Carlo methods to the renormalization-group study of static and dynamic critical phenomena within the framework of a kinetic Ising model. Simple calculations demonstrating these ideas are presented.

We have measured the linear polarization correlation between the two photons from the $7{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\to 6{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\to 6{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ cascade of ${\mathrm{Hg}}^{200}$. The results were used to evaluate Freedman's version of the Bell inequality, $\delta <~0$. Our result is ${\delta }_{\exp }=+0.046\mathrm{}\pm 0.014$, in clear violation of the inequality and in excellent agreement with the quantum mechanical prediction, ${\delta }_{\mathrm{QM}}=+0.044\mathrm{}\pm 0.007$. An important feature of the experiment was the explicit measurement of the initial density matrix for the cascading atoms.

We present a simple equation of state for classical two-component ionic plasmas in a rigid, uniform background based on the numerical solution of the coupled hypernetted-chain integral equations for the pair distribution functions. The results are used to study the phase separation of pressure-ionized H-He and H-Li mixtures.

Various nonlinear evolution equations that have been solved by the two-component inverse-scattering method are shown to be associated with the motion of certain simple types of helical curves. The linear eigenvalue problem that is usually postulated for solving these equations is found to follow quite incidentally from the standard intrinsic equations that govern the motion of space curves.

We report on the first observation of Fresnel diffraction of a beam of unpolarized slow neutrons by individual ferromagnetic domain boundaries. The observed occurrence of destructive interference in the experiment demonstrates that the phase of a spinor wave function changes by a factor of - 1 when the particle described by that wave function is rotated by an odd multiple of $2\pi$ radians.

The detection of Mg ii fine structure and hydrogen hyperfine absorption lines toward the radio source AO 0235 + 164 allows us to place upper limits on the variability of three products of the fine-structure constant, the nuclear $g$ factor of the proton, and the ratio of electron to proton mass, viz. $\frac{{\alpha }^2{g}_{p}m}{M}$ $\frac{g_{p}m}{M}$, and $\alpha$. Since the spectral lines are observed at a high red shift, $z=0.5\mathrm{}$, the limits obtained on the variation with time of these quantities (adopting $z$ as a measure of the Hubble expansion) apply over at least 35% of the age of the universe.