10 research outputs found
{}-Gauge Structures and their Anomalies:An Algebraic Approach
Starting from flat two-dimensional gauge potentials we propose the notion of
-gauge structure in terms of a nilpotent BRS differential algebra.
The decomposition of the underlying Lie algebra with respect to an
subalgebra is crucial for the discussion conformal covariance, in particular
the appearance of a projective connection. Different embeddings lead to
various -gauge structures. We present a general soldering procedure
which allows to express zero curvature conditions for the -currents
in terms of conformally covariant differential operators acting on the gauge fields and to obtain, at the same time, the complete nilpotent BRS
differential algebra generated by -currents, gauge fields and the
ghost fields corresponding to -diffeomorphisms. As illustrations we
treat the cases of itself and to the two different embeddings
in , {\it viz.} the - and -gauge
structures, in some detail. In these cases we determine algebraically -anomalies as solutions of the consistency conditions and discuss their
Chern-Simons origin.Comment: 46 pages,LaTe
W-algebras from symplectomorphisms
It is shown how -algebras emerge from very peculiar canonical
transformations with respect to the canonical symplectic structure on a compact
Riemann surface. The action of smooth diffeomorphisms of the cotangent bundle
on suitable generating functions is written in the BRS framework while a
-symmetry is exhibited. Subsequently, the complex structure of the symmetry
spaces is studied and the related BRS properties are discussed. The specific
example of the so-called -algebra is treated in relation to some other
different approaches.Comment: LaTex, 25 pages, no figures, to appear in Journ. Math. Phy
Polyakov soldering and second order frames : the role of the Cartan connection
The so-called "soldering" procedure performed by A.M. Polyakov in [1] for a
SL(2,R)-gauge theory is geometrically explained in terms of a Cartan connection
on second order frames of the projective space RP^1. The relationship between a
Cartan connection and the usual (Ehresmann) connection on a principal bundle
allows to gain an appropriate insight into the derivation of the genuine "
diffeomorphisms out of gauge transformations" given by Polyakov himself.Comment: Accept\'e pour publication dans Lett. Math. Phy
Electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with nuclei
We review and summarize recent theoretical and experimental work on electron
spin dynamics in quantum dots and related nanostructures due to hyperfine
interaction with surrounding nuclear spins. This topic is of particular
interest with respect to several proposals for quantum information processing
in solid state systems. Specifically, we investigate the hyperfine interaction
of an electron spin confined in a quantum dot in an s-type conduction band with
the nuclear spins in the dot. This interaction is proportional to the square
modulus of the electron wave function at the location of each nucleus leading
to an inhomogeneous coupling, i.e. nuclei in different locations are coupled
with different strength. In the case of an initially fully polarized nuclear
spin system an exact analytical solution for the spin dynamics can be found.
For not completely polarized nuclei, approximation-free results can only be
obtained numerically in sufficiently small systems. We compare these exact
results with findings from several approximation strategies.Comment: 26 pages, 9 figures. Topical Review to appear in J. Phys.: Condens.
Matte
The dressing field method of gauge symmetry reduction, a review with examples
International audienceGauge symmetries are a cornerstone of modern physics but they come with technical difficulties when it comes to quantization, to accurately describe particles phenomenology or to extract observables in general. These shortcomings must be met by essentially finding a way to effectively reduce gauge symmetries. We propose a review of a way to do so which we call the dressing field method. We show how the BRST algebra satisfied by gauge fields, encoding their gauge transformations, is modified. We outline noticeable applications of the method, such as the electroweak sector of the Standard Model and the local twistors of Penrose