In the presence of long-time memory effects, Fick's law must be modified by replacing the diffusion coefficient by a convolution over time of the velocity autocorrelation function. This leads to a convergent Chapman-Enskog expansion in a fluid provided the proper reference frame is taken in the presence of hydrodynamic motion.

It is shown that the solution of Einstein's equations recently found by Kundu can be written in the same form of the Van Stockum solution with the use of an appropriate transformation.

By letting the lattice spacing $a$ approach zero as the order $n$ of perturbation theory increases in such a way that the product $\mathrm{na}$ remains fixed, we substantially improve the numerical predictions. The approximation scheme described here is superior to conventional Padé approximation.

Under the assumption that there are no bound states, a singular linear integral equation for the scattering wave function is derived whose kernel contains the scattering amplitude only. The equation is used to obtain a representation of the potential in terms of the scattering amplitude and the wave function. The final result is a three-dimensional analog of the Marchenko equation.

All the equilibrium states of the two-dimensional Ising system are convex combinations of the pure phases and, as such, translation invariant. This has been rigorously proven and is related to the instability of phase boundary lines with respect to thermal fluctuations. While in higher dimensions stable phase coexistence is known to occur, the instability is expected to be typical of two-dimensional systems.

We suggest that the Monte Carlo renormalization group, when combined with the type of cell-spin transformation introduced by van Leeuwen, should be a powerful tool in the study of Ising models with $n>~2$. Numerical results are presented for the Baxter model and the Ising model with nearest- and next-nearest-neighbor interactions on a square lattice.

For isolated gravitating systems of physical interest, the difference between the Arnowitt-Deser-Misner four-momentum and the Bondi four-momentum associated with a retarded instant of time is shown to equal the four-momentum carried away by the gravitational radiation emitted between infinite past and the given retarded instant.

Based on the manifestly covariant canonical formalism of quantum gravity, it is proved that gravitons must be exactly massless.

An algebra of forms in Minkowski space has been constructed. A multiplication between forms is defined as an extension of the quaternionic multiplications. The algebra obtained is associative with respect to this multiplication of order 16. Duality is expressed as (new) multiplication by a basis element. Vector identities in the algebra lead to a number of new trace identities. A new derivative operator expresses the four Maxwell equations in an especially transparent form.

A new value for the fine-structure constant has been obtained from a new measurement of the gyromagnetic ratio of the proton. The result, ${{\gamma }_p}^{\prime }{\left(\mathrm{low}\right)}_{\mathrm{NBS}}=2.675\mathrm{}13229\left(57\right)\mathrm{}\times {10}^8$ ${\mathrm{s}}^{-1\mathrm{}}$ ${\mathrm{T}}_{\mathrm{NBS}}^{-1\mathrm{}}$ (0.21 ppm), is used to derive ${\alpha }^{-1\mathrm{}}=137.035\mathrm{}963\left(15\right)\mathrm{}$ (0.11 ppm). This value of ${\alpha }^{-1\mathrm{}}$ is (0.33±0.14) ppm less than the value of ${\alpha }^{-1\mathrm{}}$ derived from measurements of the anomalous magnetic moment of the electron, $a_e$, and its current best quantum electrodynamics theoretical estimate.

It is shown that the adoption of the hydrodynamical viewpoint in quantum mechanics provides a way to explain experimental results while giving electromagnetic potentials no more physical significance than they have in classical physics.

We present here a new approach to nonrelativistic perturbation theory. We show that in problems reducible to one dimension, the energy shifts and wave-function corrections, including corrections to the position of the nodes, to any order, can be expressed in quadrature in a hierarchy scheme. The second-order energy shift calculated is explicitly shown to be equivalent to that in the ordinary Rayleigh-Schrödinger theory.

Numerical studies by Betts and Oitmaa have led those authors to conjecture that in the $\mathrm{XY}$ model the ground-state magnetization $M_z$ is zero. This is a model of spins on a lattice with interactions $-J({S_n}^x{S_m}^x+{S_n}^y{S_m}^y)$, that can also describe a hard-sphere boson fluid. In the present note I prove the conjecture for arbitrary spins $\mathcal{S}=\frac{1}{2}, 1, \frac{3}{2}, \dots$ for positive $J$, and treat various generalizations.

A sum rule is derived from the connection of the critical specific heat with the critical correlation function in the disordered symmetric state. The "Ornstein-Zernike hole" which appears above the critical point must, by virtue of this sum rule, be canceled exactly by the "Fisher-Langer tail." It follows that the anomalous dimension index $\eta$ is fixed by the shape of the spectral function. A spectral function satisfying certain general properties yields $\eta \approx 0.04$.

Analysis of the high-temperature series expansions of a continuous-spin Ising model (i.e., a lattice $\lambda :{{\varphi }^4:}_d$ field theory) indicates that the strong-coupling limit of $\lambda :{{\varphi }^4:}_3$ is distinct from the critical-point theory of the continuous-spin Ising model for sufficiently Ising-like spin distributions. In four dimensions we find that the $\lambda :{\varphi }^4:$ field theory is trivial.

An analysis of $g-2\mathrm{}$ and lifetime measurements for electrons and muons at various velocities is used to compare the transformation of time, electromagnetic field, and mass in moving coordinate systems and to check the Thomas precession. The data are in good agreement with the special theory of relativity.

We report a verification of the theory of special relativity at a value of $\gamma \approx 2.5\times {10}^4$ based upon a comparison of electron $g-2\mathrm{}$ measurements at meV and GeV kinetic energies. Specially we obtain a measure of the equivalence between the quantities $\gamma \equiv {(1-{\beta }^2)}^{-\frac{1}{2}}$ and $\tilde{\gamma }\equiv \left(\frac{p}{m_0}\right)\frac{\mathrm{dp}}{\mathrm{dE}}$.

An expression for the Kolmogorov entropy has been derived. Excellent agreement between a probability description and direct dynamical computations has been found.

Quantum stochasticity (the nature of wave functions and eigenvalues when the short-wave-limit Hamiltonian has stochastic trajectories) is studied for the two-dimensional Helmsholtz equation with "stadium" boundary. The eigenvalue separations have a Wigner distribution (characteristic of a random Hamiltonian), in contrast to the clustering found for a separable equation. The eigenfunctions exhibit a random pattern for the nodal curves, with isotropic distribution of local wave vectors.

This paper presents a group-theoretic explanation of the geometric interpretation of solitons due to Lamb and Lund.