Wave-function and level statistics of random two-dimensional gauge fields

Canonical Quantization of Two Dimensional Gauge Fields

SU(N) gauge fields on a cylindrical spacetime are canonically quantized via two routes revealing almost equivalent but different quantizations. After removing all continuous gauge degrees of freedom, the canonical coordinate Aμ (in the Cartan subalgebra h) is quantized. The compact route, as in lattice gauge theory, quantizes the Wilson loop W , projecting out gauge invariant wavefunctions on t...

Level statistics for two-dimensional oscillators

We consider the level statistics of two-dimensional harmonic oscillators with incommensurable frequencies, which are known to have picket-fence type spectra. We propose a parametric representation for the level-spacing distribution and level-number variance, and study the variation of the parameters with the frequency ratio and the size of the spectra. By introducing an anharmonic perturbation,...

Statistics of Number Fields and Function Fields

We discuss some problems of arithmetic distribution, including conjectures of Cohen-Lenstra, Malle, and Bhargava; we explain how such conjectures can be heuristically understood for function fields over finite fields, and discuss a general approach to their proof in the function field context based on the topology of Hurwitz spaces. This approach also suggests that the Schur multiplier plays a ...

Line Transects of Two Dimensional Random Fields: Estimation and Design

In line transect sampling, data are collected continuously along the path travelled. These data are then used to estimate some characteristic of an entire region. We model the characteristic of the region as a linear functional of Z(), a realization of a random eld, and our data as the values of Z(x) for x along the path. We study how to estimate the characteristic of interest and how to choose...

Two - dimensional causal dynamical triangulations with gauge fields