COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Abelian and non-Abelian Hopfions in all odd dimensions

## Abelian and non-Abelian Hopfions in all odd dimensionsAdd to your list(s) Download to your calendar using vCal - Tchrakian, T (DIAS)
- Friday 07 December 2012, 11:40-12:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Topological Dynamics in the Physical and Biological Sciences Hopfions are field configurations of scalar matter systems characterised prominently by the fact that they describe knots in configuration space. Like the ‘usual solitons’, e.g. Skyrmions, monopoles, vortices and instantons, Hopfions are static and finite energy solutions that are stabilised by a topological charge, which supplies the energy lower bound. In contrast to the ‘usual solitons’ however, the topological charge of Hopfions is not the volume integral of a total divergence. While the topological charge densities of the ‘usual solitons’, namely the Chern-Pontryagin (CP) densities or their descendants, are total divergence, the corresponding quantities for Hopfions are the Chern-Simons (CS) densities which are not total divergence. Subject to the appropriate symmetries however, these CS densities do reduce to total divergence and become candidates for topological charges. Thus, Hopfion field are necessarily subject to the appropriate symmetry to decsribe knots, excluding spherically symmetry, in contrast to the ‘usual solitons’. The construction of these CS densities is enabled by employing complex nonlinear sigma models, which feature composite connections. The CS densities are defined in terms of these connections and their curvatures. (In some dimensions the complex sigma model can be equivalent to a real sigma model, e.g. in D=3 Skyrme-Fadde’ev O(3) model and the corresponding CP^1 model.) It is natural to propose Hopfion fields in all odd space dimensions where a CS density can be defined. This covers both Abelian and non-Abelian theories, namely empolying projective-complex and Grassmannian models, respectively. It is in this sense that we have used the terminology of Abelian and non-Abelian Hopfions. Explicit field configurations displaying the appropriate symmetries and specific asymptotic behaviours in several (higher) dimensions are proposed, and it is verified that for these configurations the CS densities do indeed become total divergence. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 1, Newton Institute
Note that ex-directory lists are not shown. |
## Other listsStatistical Laboratory Graduate Seminars Africa Research Forum POLIS Staff and PhD Student Colloquium Talk on the invention of the chronograph Regional Zebrafish meeting Enterprise Tuesday 2010/2011## Other talks"The integrated stress response – a double edged sword in skeletal development and disease" Fundamental Limits to Volcanic Cooling and its Implications for Past Climate on Earth Climate Change Uncertainty, Adaptation, and Growth TO A TRILLION AND BEYOND: THE FUTURE OF COMPUTING AND THE INTERNET OF THINGS - The IET Cambridge Prestige Lecture Electrophysiological approaches in Lewy body dementia: helpful or not? Phenotypic changes induced by stress and developmental reprogramming in plants Plant host-pathogen coevolution and exploring local adaptation of an Arabidopsis thaliana complex Resistance gene locus TBC Towards bulk extension of near-horizon geometries Autumn Cactus & Succulent Show 70th Anniversary Celebration Remarks on Nahm's equations Attentional episodes and cognitive control |