393 research outputs found
Exact Solution of Noncommutative Field Theory in Background Magnetic Fields
We obtain the exact non-perturbative solution of a scalar field theory
defined on a space with noncommuting position and momentum coordinates. The
model describes non-locally interacting charged particles in a background
magnetic field. It is an exactly solvable quantum field theory which has
non-trivial interactions only when it is defined with a finite ultraviolet
cutoff. We propose that small perturbations of this theory can produce solvable
models with renormalizable interactions.Comment: 9 Pages AMSTeX; Typos correcte
Explicit solution of the (quantum) elliptic Calogero-Sutherland model
We derive explicit formulas for the eigenfunctions and eigenvalues of the
elliptic Calogero-Sutherland model as infinite series, to all orders and for
arbitrary particle numbers and coupling parameters. The eigenfunctions obtained
provide an elliptic deformation of the Jack polynomials. We prove in certain
special cases that these series have a finite radius of convergence in the nome
of the elliptic functions, including the two particle (= Lam\'e) case for
non-integer coupling parameters.Comment: v1: 17 pages. The solution is given as series in q but only to low
order. v2: 30 pages. Results significantly extended. v3: 35 pages. Paper
completely revised: the results of v1 and v2 are extended to all order
Anomalies and Schwinger terms in NCG field theory models
We study the quantization of chiral fermions coupled to generalized Dirac
operators arising in NCG Yang-Mills theory. The cocycles describing chiral
symmetry breaking are calculated. In particular, we introduce a generalized
locality principle for the cocycles. Local cocycles are by definition
expressions which can be written as generalized traces of operator commutators.
In the case of pseudodifferential operators, these traces lead in fact to
integrals of ordinary local de Rham forms. As an application of the general
ideas we discuss the case of noncommutative tori. We also develop a gerbe
theoretic approach to the chiral anomaly in hamiltonian quantization of NCG
field theory.Comment: 30 page
Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation
We construct elliptic multi-soliton solutions of the spin non-chiral
intermediate long-wave (sncILW) equation with periodic boundary conditions.
These solutions are obtained by a spin-pole ansatz including a dynamical
background term; we show that this ansatz solves the periodic sncILW equation
provided the spins and poles satisfy the elliptic -type spin Calogero-Moser
(sCM) system with certain constraints on the initial conditions. The key to
this result is a B\"{a}cklund transformation for the elliptic sCM system which
includes a non-trivial dynamical background term. We also present solutions of
the sncILW equation on the real line and of the spin Benjamin-Ono equation
which generalize previously obtained solutions by allowing for a non-trivial
background term.Comment: 33 page
Volcanic ash as fertiliser for the surface ocean
Iron is a key limiting micro-nutrient for marine primary productivity. It can be supplied to the ocean by atmospheric dust deposition. Volcanic ash deposition into the ocean represents another external and so far largely neglected source of iron. This study demonstrates strong evidence for natural fertilisation in the iron-limited oceanic area of the NE Pacific, induced by volcanic ash from the eruption of Kasatochi volcano in August 2008. Atmospheric and oceanic conditions were favourable to generate a massive phytoplankton bloom in the NE Pacific Ocean which for the first time strongly suggests a connection between oceanic iron-fertilisation and volcanic ash supply
BRST symmetry of SU(2) Yang-Mills theory in Cho--Faddeev--Niemi decomposition
We determine the nilpotent BRST and anti-BRST transformations for the
Cho--Faddeev-Niemi variables for the SU(2) Yang-Mills theory based on the new
interpretation given in the previous paper of the Cho--Faddeev-Niemi
decomposition. This gives a firm ground for performing the BRST quantization of
the Yang--Mills theory written in terms of the Cho--Faddeev-Niemi variables. We
propose also a modified version of the new Maximal Abelian gauge which could
play an important role in the reduction to the original Yang-Mills theory.Comment: 11 pages, no figure; Introduction improved, 3 references adde
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