A Short Range Force

Gravitomagnetic and gravitoelectric forces have been studied for sometime and tests for detecting such forces arising from the earth, are under way. We apply similar considerations at the level of elementary particles in a formulation using General Relativity, and deduce the presence of short range forces. A possible candidate could be the somewhat recently detected but otherwise mysterious short range $B_{(3)}$ force, mediated by massive "photons".Comment: 4 pages, TeX, Based on the paper in the Fifth International Symposium, Frontiers of Fundamental Physic

Generalized Drinfeld-Sokolov Hierarchies, Quantum Rings, and W-Gravity

We investigate the algebraic structure of integrable hierarchies that, we propose, underlie models of $W$-gravity coupled to matter. More precisely, we concentrate on the dispersionless limit of the topological subclass of such theories, by making use of a correspondence between Drinfeld-Sokolov systems, principal $s\ell(2)$ embeddings and certain chiral rings. We find that the integrable hierarchies can be viewed as generalizations of the usual matrix Drinfeld-Sokolov systems to higher fundamental representations of $s\ell(n)$. The underlying Heisenberg algebras have an intimate connection with the quantum cohomology of grassmannians. The Lax operators are directly given in terms of multi-field superpotentials of the associated topological LG theories. We view our construction as a prototype for a multi-variable system and suspect that it might be useful also for a class of related problems.Comment: 34p, harvmac/lanlmac with hyperlinks, 2 uuencoded PostScript figures appended, CERN-TH.6988/93. (streamlined version that incorporates recent results on $W$-ground ring spectra

Quantum and Classical Aspects of Deformed c=1c=1 Strings.

The quantum and classical aspects of a deformed $c=1$ matrix model proposed by Jevicki and Yoneya are studied. String equations are formulated in the framework of Toda lattice hierarchy. The Whittaker functions now play the role of generalized Airy functions in $c<1$ strings. This matrix model has two distinct parameters. Identification of the string coupling constant is thereby not unique, and leads to several different perturbative interpretations of this model as a string theory. Two such possible interpretations are examined. In both cases, the classical limit of the string equations, which turns out to give a formal solution of Polchinski's scattering equations, shows that the classical scattering amplitudes of massless tachyons are insensitive to deformations of the parameters in the matrix model.Comment: 52 pages, Latex

Spin-orbit splittings in heavy-light mesons and Dirac equation

The spin-orbit splitting in heavy-light mesons is seen to be suppressed experimentally. It is shown that it can be understood qualitatively in the frame work of Dirac theory. An alternative derivation of a relativistic dynamical symmetry for the Dirac Hamiltonian, which suppresses spin orbit splitting, is also given. However it is shown that such a symmetry is not needed since the spin-orbit splitting in Dirac theory with Coulomb like potential (as is the case for the one gluon exchange potential in pQCD) is small anyway.Comment: 9 pages, 1 fi