Real spinors and real Dirac equation

We reexamine the minimal coupling procedure in the Hestenes' geometric algebra formulation of the Dirac equation, where spinors are identified with the even elements of the real Clifford algebra of spacetime. This point of view, as we argue, leads naturally to a non-Abelian generalisation of the electromagnetic gauge potential.Comment: 10 pages, 3 figure

Braiding Interactions in Anyonic Quantum Walks

The anyonic quantum walk is a dynamical model describing a single anyon propagating along a chain of stationary anyons and interacting via mutual braiding statistics. We review the recent results on the effects of braiding statistics in anyonic quantum walks in quasi-one dimensional ladder geometries. For anyons which correspond to spin-1/2 irreps of the quantum groups $SU(2)_k$, the non-Abelian species $(1<k<\infty)$ gives rise to entanglement between the walker and topological degrees of freedom which is quantified by quantum link invariants over the trajectories of the walk. The decoherence is strong enough to reduce the walk on the infinite ladder to classical like behaviour. We also present numerical results on mixing times of $SU(2)_2$ or Ising model anyon walks on cyclic graphs. Finally, the possible experimental simulation of the anyonic quantum walk in Fractional Quantum Hall systems is discussed.Comment: 13 pages, submitted to Proceedings of the 2nd International Conference on Theoretical Physics (ICTP 2012

Statistical dynamics of a non-Abelian anyonic quantum walk

We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants. We find that asymptotically a mobile Ising anyon becomes so entangled with its environment that its statistical dynamics reduces to a classical random walk with linear dispersion in contrast to particles with Abelian statistics which have quadratic dispersion.Comment: 7 pages, 5 figure

Cytokinin metabolism in maize: Novel evidence of cytokinin abundance, interconversions and formation of a new trans-zeatin metabolic product with a weak anticytokinin activity

Cytokinins (CKs) are an important group of phytohormones. Their tightly regulated and balanced levels are essential for proper cell division and plant organ development. Here we report precise quantification of CK metabolites and other phytohormones in maize reproductive organs in the course of pollination and kernel maturation. A novel enzymatic activity dependent on NADP(+) converting trans-zeatin (tZ) to 6-(3-methylpyrrol-1-yl)purine (MPP) was detected. MPP shows weak anticytokinin properties and inhibition of CK dehydrogenases due to their ability to bind to an active site in the opposite orientation than substrates. Although the physiological significance of tZ side-chain cyclization is not anticipated as the MPP occurrence in maize tissue is very low, properties of the novel CK metabolite indicate its potential for utilization in plant in vitro tissue culture. Furthermore, feeding experiments with different isoprenoid CKs revealed distinct preferences in glycosylation of tZ and cis-zeatin (cZ). While tZ is preferentially glucosylated at the N9 position, cZ forms mainly O-glucosides. Since O-glucosides, in contrast to N9-glucosides, are resistant to irreversible cleavage catalyzed by CK dehydrogenases, the observed preference of maize CK glycosyltransferases to O-glycosylate zeatin in the cis-position might be a reason why cZ derivatives are over-accumulated in different maize tissues and organs