Self-Duality and Maximally Helicity Violating QCD Amplitudes

I review some recent work that describes the close analogy between self-dual Yang--Mills amplitudes and QCD amplitudes with external gluons of positive helicity. This analogy is carried at tree level for amplitudes with two external quarks and up to one-loop for amplitudes involving only external gluons.Comment: 10 pages, LaTeX, no figures. Proceedings of the "Low Dimensional Field Theory Workshop, Telluride." Some ideas proposed by Duff and Isham have been include

Poincar\'e Gauge Theory for Gravitational Forces in (1+1) Dimensions

We discuss in detail how string-inspired lineal gravity can be formulated as a gauge theory based on the centrally extended Poincar\'e group in $(1+1)$ dimensions. Matter couplings are constructed in a gauge invariant fashion, both for point particles and Fermi fields. A covariant tensor notation is developed in which gauge invariance of the formalism is manifest.Comment: 43 p., CTP#216

Temperature Expansions for Magnetic Systems

We derive finite temperature expansions for relativistic fermion systems in the presence of background magnetic fields, and with nonzero chemical potential. We use the imaginary-time formalism for the finite temperature effects, the proper-time method for the background field effects, and zeta function regularization for developing the expansions. We emphasize the essential difference between even and odd dimensions, focusing on $2+1$ and $3+1$ dimensions. We concentrate on the high temperature limit, but we also discuss the $T=0$ limit with nonzero chemical potential.Comment: 25 pages, RevTe

Extended de Sitter Theory of Two Dimensional Gravitational Forces

We present a simple unifying gauge theoretical formulation of gravitational theories in two dimensional spacetime. This formulation includes the effects of a novel matter-gravity coupling which leads to an extended de Sitter symmetry algebra on which the gauge theory is based. Contractions of this theory encompass previously studied cases.Comment: 19pp, no figs., CTP 2228, UCONN-93-

Spatial Geometry of the Electric Field Representation of Non-Abelian Gauge Theories

A unitary transformation \Ps [E]=\exp (i\O [E]/g) F[E] is used to simplify the Gauss law constraint of non-abelian gauge theories in the electric field representation. This leads to an unexpected geometrization because \o^a_i\equiv -\d\O [E]/\d E^{ai} transforms as a (composite) connection. The geometric information in \o^a_i is transferred to a gauge invariant spatial connection \G^i_{jk} and torsion by a suitable choice of basis vectors for the adjoint representation which are constructed from the electric field $E^{ai}$. A metric is also constructed from $E^{ai}$. For gauge group $SU(2)$, the spatial geometry is the standard Riemannian geometry of a 3-manifold, and for $SU(3)$ it is a metric preserving geometry with both conventional and unconventional torsion. The transformed Hamiltonian is local. For a broad class of physical states, it can be expressed entirely in terms of spatial geometric, gauge invariant variables.Comment: 16pp., REVTeX, CERN-TH.7238/94 (Some revision on Secs.3 and 5; one reference added

Boundary states for moving D-branes

We determine the boundary state for both the NS-NS and R-R sectors of superstring theory. We show how they are modified under a boost. The boosted boundary state is then used for computing the interaction of two D-branes moving with constant velocity reproducing with a completely different method a recent calculation by Bachas.Comment: 10 pages, LaTeX, no figures; Eqs. (47) and (48) correcte