An argument leading from the Lorentz invariance of the Lagrangian to the introduction of the
gravitational field is presented. Utiyama's discussion is extended by considering the 10‐
parameter group of inhomogeneous Lorentz transformations, involving variation of the …

Kruskal's transformation of the Schwarzschild metric is generalized to apply to the stationary,
axially symmetric vacuum solution of Kerr, and is used to construct a maximal analytic
extension of the latter. In the low angular momentum case, a2< m2, this extension consists of …

A method of solution for the''derivative nonlinear Schrödinger equation''iqt=− qxx±i (q* q2) x
is presented. The appropriate inverse scattering problem is solved, and the one‐soliton
solution is obtained, as well as the infinity of conservation laws. Also, we note that this …

We develop here two aspects of the connection between nonlinear partial differential
equations solvable by inverse scattering transforms and nonlinear ordinary differential
equations (ODE) of P‐type (ie, no movable critical points). The first is a proof that no solution …

A set of quasi-probability distribution functions which give the correct quantum mechanical
marginal distributions of position and momentum is studied. The phase-space distribution
does not have to be bilinear in the state function. The Wigner distribution is a special case. A …

The following results are proved for a system of Ising spins σi=±1 in zero magnetic field
coupled by a purely ferromagnetic interaction of the form− Σi< j Jijσiσj with Jij≥ 0, for
arbitrary crystal lattice and range of interaction:(1) The binary correlation functions< σkσl> …

An action principle technique for the direct computation of expectation values is described
and illustrated in detail by a special physical example, the effect on an oscillator of another
physical system. This simple problem has the advantage of combining immediate physical …

A new class of empty‐space metrics is obtained, one member of this class being a natural
generalization of the Schwarzschild metric. This latter metric contains one arbitrary
parameter in addition to the mass. The entire class is the set of metrics which are …

The quantum‐mechanical problems of N 1‐dimensional equal particles of mass m
interacting pairwise via quadratic (``harmonical'') and/or inversely quadratic (``centrifugal'')
potentials is solved. In the first case, characterized by the pair potential ¼mω2 (xi− xj) 2+ g …

Formulas are obtained for the mean first passage times (as well as their dispersion) in
random walks from the origin to an arbitrary lattice point on a periodic space lattice with
periodic boundary conditions. Generally this time is proportional to the number of lattice …