Abstract We study a noncommutative nonrelativistic theory in 2+1 dimensions of a scalar field coupled to the Chern-Simons field. In the commutative situation this model has been used to simulate the Aharonov-Bohm effect in the field theory context. We verified that, contrarily to the commutative result, the inclusion of a quartic self-interaction of the scalar field is not necessary to secure t...

The SDLCQ regularization is known to explicitly preserve supersymmetry in 1+1 dimensions. To test this property in higher dimensions, we consider supersymmet-ric Yang-Mills theory on R × S 1 × S 1. In particular, we choose one of the compact directions to be light-like and another to be space-like. This theory is totally finite , and thus we can solve for bound state wave functions and masses n...

There have been a number of previous successful efforts that show how fuzzy logic concepts have homomorphic-like stochastic correspondences, utilizing one-point coverages of appropriately constructed random sets. Independent of this and fuzzy logic considerations in general, boolean relational event algebra (BREA) has been introduced within a stochastic setting for representing prescribed compo...

Exploiting a 3+1 analysis of the so-called Mars-Simon tensor, conditions on a vacuum initial data set ensuring that its development is isometric to a subset of the Kerr spacetime are found. These conditions are expressed in terms of the vanishing of a positive scalar function defined on the initial data hypersurface. Applications of this result are discussed. PACS numbers: 04.20.Ex, 04.20-q, 04...

A quantile binary classifier uses the rule: Classify x as +1 if P (Y = 1|X = x) ≥ τ , and as −1 otherwise, for a fixed quantile parameter τ ∈ [0, 1]. It has been shown that Support Vector Machines (SVMs) in the limit are quantile classifiers with τ = 12 . In this paper, we show that by using asymmetric cost of misclassification SVMs can be appropriately extended to recover, in the limit, the qu...

The BP Deepwater Horizon oil spill of 2010 has focused considerable attention on the potential liability and the operating conduct of big oil companies. This paper shows that limiting the ability of a company to insure and diversify its risks creates incentives to internalize the welfare effects of catastrophic events, leading to a welfare improvement. We model an economy with complete financia...

We develope the dual picture for Quantum Electrodynamics in 3+1 dimensions. It is shown that the photon is massless in the Coulomb phase due to spontaneous breaking of the magnetic symmetry group. The generators of this group are the magnetic fluxes through any infinite surface Φ S. The order parameter for this symmetry breaking is the operator V (C) which creates an infinitely long magnetic vo...

The equations of motion for a fully ionized hydrogenic plasma in applied coaxial electric and magnetic fields are analyzed, where the term for the Hall effect in the generalized Ohm’s law equation picks up a factor of 1/2 relative to its usual expression. Magnetization of the medium is incorporated through the decomposition of the Hall term and the inclusion of the magnetization force, which is...

Since the gauge group underlying 2+1-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately choosing the measure that features in the definition of the loop transform. Thus, “old-fashioned” loop representations – based on ordinary loops – do exist. I...

We have performed high precision measurements of level splitting and level shifts of an excited atomic state in the presence of an intense optical field. Such measurements are important to the understanding of the details of atom-field interaction and in the development of high precision optical clocks. The level we studied is an isolated 2 single magnetic sublevel 3 P3/2 (F= 3, 2m F = 3) in so...