Physical Sciences and Mathematics | Open Access Articles

Generating Unbiased Ratio And Regression Estimators, William (Bill) H. Williams

Publications and Research

Standard ratio and regression are only conditionally unbiased. The paper uses split sample techniques to develop unbiased versions.

Go to article

Kähler-Chern-Simons Theory And Symmetries Of Anti-Self-Dual Gauge Fields, V. Parameswaran Nair, Jeremy Schiff

Publications and Research

Kähler-Chern-Simons theory, which was proposed as a generalization of ordinary Chern-Simons theory, is explored in more detail. The theory describes anti-self-dual in-stantons on a four-dimensional Kähler manifold. The phase space is the space of gauge potentials, whose symplectic reduction by the constraints of anti-self-duality leads to the moduli space of instantons. We show that infinitesimal Bäcklund transformations, previously related to "hidden symmetries" of instantons, are canonical transformations generated by the anti-self-duality constraints. The quantum wave functions naturally lead to a generalized Wess-Zumino-Witten action, which in turn has associated chiral current algebras. The dimensional reduction of the anti-self-duality equations leading to …

Go to article

Relativistic Wave Equation For Anyons, R. Jackiw, V. Parameswaran Nair

Publications and Research

Construction of one-particle states as unitary representations of the Poincare algebra in 2 + 1 dimensions shows that an anyon has one polarization state. However, for nonzero spin manifestly linear and covariant realizations of Lorentz transformations require more than one field component, and an infinite number is needed when the value of spin is not an integer or half-integer. We discuss the relation between these two aspects of Poincare symmetry. In particular, we construct a relativistic equation for anyons where the number of physical polarizations is reduced to one by virtue of a gauge symmetry or equivalent constraint.

Go to article