The production of gravitons in a homogeneous, isotropic, spatially flat universe containing radiation and a small admixture of cold baryons is studied by an effective-potential method which takes into account the back reaction of the produced gravitons on the geometry. The total probability per unit volume to produce a pair of gravitons is finite and has a very small value for a universe with parameters corresponding to my own.

Vibrational-dephasing times have been measured in mixtures of liquid ${\mathrm{N}}_2$ and Ar. The correlation time of the molecular motion initiating the dephasing process is calculated to be 2.2 and 4.6 ps in pure ${\mathrm{N}}_2$ and pure Ar, respectively. These rather long correlation times suggest that the dephasing results from the average force field determined by the number of nearest-neighbor molecules.

We formulate the problem of colliding plane gravitational waves with two polarizations as the harmonic mappings of Riemannian manifolds and construct an exact solution of the vacuum Einstein field equations describing the interaction of colliding impulsive gravitational waves which in the limit of collinear polarization reduces to the solution of Khan and Penrose.

Using the molecular-dynamics technique, we establish solitonlike properties of heat pulses in a lattice-dynamic model when the ambient temperature is in the second-sound regime.

We present the gauge theory of the graded conformal group. It contains four real fields with spins 2, $\frac{3}{2}$, 1, and ½. The theory is invariant under local proper conformal, scale, chiral, gravitational, and supersymmetry transformations. This is the first of a class of superunified field theories, possessing $\mathrm{U}\mathrm{}\left(n\right)\mathrm{}$ rather than $\mathrm{O}\mathrm{}\left(n\right)\mathrm{}$ internal gauge symmetries and without a cosmological constant. Unitarity, renormalizability, and asymptotic states and the cancellation of some complicated higher-order terms in one of the two supersymmetry variations remain to be investigated.

We present rigorous perturbation results for the dynamics of the classical nearest-neighbor Heisenberg chain, using the temperature as a small parameter. The lifetime and the frequency shift of the spin waves are determined. For the antiferromagnet we find that there is a region of wave vectors close to the zone boundary where the dynamical scaling fails and we argue that this is a general property of the Heisenberg chain close to $T=0\mathrm{}$.

Recent observations of regularly pulsating x-ray sources in binary star systems are analyzed in the framework of the "emission" theory of light. Assuming that light emitted by a source moving at velocity $v$ with respect to an observer has a speed $c^{\prime }=c+kv$ in the observer's rest frame, we find that the arrival time of pulses from the binary x-ray sources implies $k<\mathrm{}2\mathrm{}\times {10}^{-9\mathrm{}}$. This appears to be the most direct and sensitive demonstration that the speed of light is independent of the velocity of the source.

Lines of critical points which emerge from the two-dimensional planar model's multicritical point are analyzed. These lines seem to be in the same universality class as both the Ashkin-Teller and the eight-vertex (8V) models' critical lines, with the multicritical point being isomorphic with the 8V model at both the points $tanh2\lambda =\frac{\sqrt{2}}{2} \mathrm{and} -1\mathrm{}$. Expansions of critical indices about these values of $\lambda$ are performed. If this analysis is right, then this work permits the evaluation of a whole class of interesting correlation functions at the critical point of the $F$ model and that of the four-state Potts model.

In the variational approach to scattering, one traditionally adopts a trial function of the form ${\mathcal{I}}_t\mathrm{}\left(r\right)={\Sigma }_i{C}_i{\varphi }_i+j_l\mathrm{}\left(r\right)+{\lambda }_{t}g\left(r\right)\mathrm{}{n}_l\mathrm{}\left(r\right),$ where the ${\varphi }_i$ are square-integrable functions, ${\lambda }_t$ is the tangent of the trial phase shift, $j_l\mathrm{}\left(r\right)\mathrm{}$ and $n_l\mathrm{}\left(r\right)\mathrm{}$ are, respectively, the regular and irregular Riccati-Bessel functions, and $g\left(r\right)\mathrm{}$ cuts $n_l\mathrm{}\left(r\right)\mathrm{}$ off at the origin. A modified form for the trial function is suggested and used in the determination of phase shifts in the static-exchange hydrogen problem.

I review arguments indicating that there is no real, physically detectable, local inertial-induction effect in general relativity, contrary to recent comments by Tittle.

A proper treatment of the continuous-time random-walk problem leads to a frequency-dependent conductivity in agreement with our earlier work.

The low-frequency fluctuations resulting from the nonlinear coupling of high-frequency fluctuations is shown to possess a $\frac{1}{f}$ noise spectrum.

We present generalized Einstein equations, invariant under scale transformations, and study several astrophysical tests. It is assumed that the dynamics of atoms or clocks used as measuring apparatus is given a priori. Connection with gauge fields and broken symmetries is made through the cosmological constant.

Solutions for the nonlinear evolution of the one-dimensional space-time and two-dimensional steady-state interaction of three wave packets in an inhomogeneous medium are presented. A transformation of the nonlinear equations allows the use of an inverse scattering transform for finding exact time-asymptotic properties of the interaction. Inhomogeneity gives a decreased action transfer in both decay and backscattering, and suppresses explosive instabilities and soliton decay above a certain threshold.

We show that the total energy in supergravity theory is nonnegative. The derivation is based on the fact that for bounded systems the Hamiltonian operator is the square of the spinor supercharge just as for globally supersymmetric systems. The result holds for any of the pure, matter-coupled, or extended versions of supergravity, except those with cosmological term for which the concept of total energy does not exist.

A class of U(1)-invariant theories in $d$ dimensions is introduced on a lattice. These theories are labeled by a simplex number $s$, with $1<~s<d$. The case with $s=1\mathrm{}$ is the $X-Y$ model; and $s=2\mathrm{}$ gives compact photodynamics. An exact duality transformation is applied to show that the U(1)-invariant theory in $d$ dimensions with simplex number $s$ is the same as a similar theory in $d$ dimensions but which is $Z_{\infty }$-invariant and has simplex number $\tilde{s}=d-s$. This dual theory describes the topological excitations of the original theory. These excitations are of dimension $\tilde{s}-1\mathrm{}$.

We separate the (decoupled) perturbation equations for the radiative components of perturbing fields of spin $s=0, \frac{1}{2}, 1, \mathrm{and} 2$ in an arbitrary type-$D$ vacuum background, realized in Plebański-Demiański coordinates.

We consider the supersymmetric Higgs effect, in which a spin-½ Goldstone fermion is transformed away by a redefinition of the supergravity fields and the spin-$\frac{3}{2}$ gauge field acquires the degrees of freedom appropriate to finite mass. More generally we discuss the consistency and physical applicability of supergravity theories with broken local supersymmetry.

A new method of exploring the contents of the renormalization-group equations for discrete spins is introduced. The equations are expanded in low-temperature series and the truncated series are used to obtain the critical exponents and critical temperature of a system. The method is demonstrated on the planar triangular Ising lattice and the critical parameters are found to be within a few percent of the exactly known values in third nonvanishing order of approximation.

An operator renormalization transformation is proposed for quantum spin systems which is manifestly basis independent and preserves the fundamental symmetries of the spin Hamiltonian. We develop a cumulant expansion suitable for noncommuting operators and illustrate the general techniques with several sample calculations.