The Effective Lagrangian of Three Dimensional Quantum Chromodynamics

We consider the low energy limit of three dimensional Quantum Chromodynamics with an even number of flavors. We show that Parity is not spontaneously broken, but the global (flavor) symmetry is spontaneously broken. The low energy effective lagrangian is a nonlinear sigma model on the Grassmannian. Some Chern--Simons terms are necessary in the lagrangian to realize the discrete symmetries correctly. We consider also another parametrization of the low energy sector which leads to a three dimensional analogue of the Wess--Zumino--Witten--Novikov model. Since three dimensional QCD is believed to be a model for quantum anti--ferromagnetism, our effective lagrangian can describe their long wavelength excitations (spin waves).Comment: 18 page

Three Dimensional Quantum Chromodynamics

The subject of this talk was the review of our study of three ($2+1$) dimensional Quantum Chromodynamics. In our previous works, we showed the existence of a phase where parity is unbroken and the flavor group $U(2n)$ is broken to a subgroup $U(n)\times U(n)$. We derived the low energy effective action for the theory and showed that it has solitonic excitations with Fermi statistic, to be identified with the three dimensional ``baryon''. Finally, we studied the current algebra for this effective action and we found a co-homologically non trivial generalization of Kac-Moody algebras to three dimensions.Comment: 7 pages, Plain TEX, talk presented by S.G. Rajeev at the XXVI INTERNATIONAL CONFERENCE ON HIGH ENERGY PHYSICS, DALLAS TX AUG. 199

Baryons as Solitons in Three Dimensional Quantum Chromodynamics

We show that baryons of three dimensional Quantum Chromodynamics can be understood as solitons of its effective lagrangian. In the parity preserving phase we study, these baryons are fermions for odd $N_c$ and bosons for even $N_c$, never anyons. We quantize the collective variables of the solitons and there by calculate the flavor quantum numbers, magnetic moments and mass splittings of the baryon. The flavor quantum numbers are in agreement with naive quark model for the low lying states. The magnetic moments and mass splittings are smaller in the soliton model by a factor of $\log {F_\pi\over N_c m_\pi}$. We also show that there is a dibaryon solution that is an analogue of the deuteron. These solitons can describe defects in a quantum anti--ferromagnet.Comment: 22 pages + 4 figures (figures not included, postscript files available upon request

Proposal for a QND which-path measurement using photons

A scheme is proposed for experimentally realizing the famous two-slit gedaenken experiment using photons. As elegantly discussed for electrons by Feynman, a particle's quantum pathways interfere to produce fringes in the probability density for the particle to be found at a particle location. If the path taken by the particle is experimentally determined, the complementarity principle says that the fringes must disappear. To carry out this experiment with photons is difficult because normally the act of determining a photon's location destroys it. We propose to overcome this difficulty by putting a type-2 optical parametric amplifier (OPA) in each arm of a Mach-Zehnder interferometer, and observing fringes at the output. An OPA responds to an input photon by increasing its probability to produce a pair of photons with polarization orthogonal to the input, the detection of which allows partial inference about the path taken by the input photon without destroying it. Thus, the measurement is of the quantum nondemolition (QND) type

Zeeman and Orbital Effects of an in-Plane Magnetic Field in Cuprate Superconductors

We discuss the effects of a magnetic field applied parallel to the Cu-O ($ab$) plane of the high $T_c$ cuprate superconductors. After briefly reviewing the Zeeman effect of the field, we study the orbital effects, using the Lawrence-Doniach model for layered superconductors as a guide to the physics. We argue that the orbital effect is qualitatively different for in-plane and inter-layer mechanisms for superconductivity. In the case of in-plane mechanisms, interlayer couplings may be modeled as a weak interlayer Josephson coupling, whose effects disappear as $H\to\infty$; in this case Zeeman dominates the effect of the field. In contrast, in the inter-layer mechanism the Josephson coupling {\em is} the driving force of superconductivity, and we argue that the in-plane field suppresses superconductivity and provides an upper bound for $H_{c2}$ which we estimate very crudely.Comment: 4 pages with 1 embedded ps figure. Manuscript submitted to the MMM'99 conferenc