12 research outputs found
Enhanced spectral discrimination through the exploitation of interface effects in photon dose data
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134954/1/mp7731.pd
Open Wilson Lines and Group Theory of Noncommutative Yang-Mills Theory in Two Dimensions
The correlation functions of open Wilson line operators in two-dimensional
Yang-Mills theory on the noncommutative torus are computed exactly. The
correlators are expressed in two equivalent forms. An instanton expansion
involves only topological numbers of Heisenberg modules and enables extraction
of the weak-coupling limit of the gauge theory. A dual algebraic expansion
involves only group theoretic quantities, winding numbers and translational
zero modes, and enables analysis of the strong-coupling limit of the gauge
theory and the high-momentum behaviour of open Wilson lines. The dual
expressions can be interpreted physically as exact sums over contributions from
virtual electric dipole quanta.Comment: 37 pages. References adde
Conformal Motions and the Duistermaat-Heckman Integration Formula
We derive a geometric integration formula for the partition function of a
classical dynamical system and use it to show that corrections to the WKB
approximation vanish for any Hamiltonian which generates conformal motions of
some Riemannian geometry on the phase space. This generalizes previous cases
where the Hamiltonian was taken as an isometry generator. We show that this
conformal symmetry is similar to the usual formulations of the
Duistermaat-Heckman integration formula in terms of a supersymmetric Ward
identity for the dynamical system. We present an explicit example of a
localizable Hamiltonian system in this context and use it to demonstrate how
the dynamics of such systems differ from previous examples of the
Duistermaat-Heckman theorem.Comment: 13 pages LaTeX, run twice. Uses epsf.tex, 2 postscript files read
directly into LaTeX file from director
Fermionic Quantum Gravity
We study the statistical mechanics of random surfaces generated by NxN
one-matrix integrals over anti-commuting variables. These Grassmann-valued
matrix models are shown to be equivalent to NxN unitary versions of generalized
Penner matrix models. We explicitly solve for the combinatorics of 't Hooft
diagrams of the matrix integral and develop an orthogonal polynomial
formulation of the statistical theory. An examination of the large N and double
scaling limits of the theory shows that the genus expansion is a Borel summable
alternating series which otherwise coincides with two-dimensional quantum
gravity in the continuum limit. We demonstrate that the partition functions of
these matrix models belong to the relativistic Toda chain integrable hierarchy.
The corresponding string equations and Virasoro constraints are derived and
used to analyse the generalized KdV flow structure of the continuum limit.Comment: 59 pages LaTeX, 1 eps figure. Uses epsf. References and
acknowledgments adde