150 research outputs found
Conformal Einstein equations and Cartan conformal connection
Necessary and sufficient conditions for a space-time to be conformal to an
Einstein space-time are interpreted in terms of curvature restrictions for the
corresponding Cartan conformal connection
Differential Calculi on Some Quantum Prehomogeneous Vector Spaces
This paper is devoted to study of differential calculi over quadratic
algebras, which arise in the theory of quantum bounded symmetric domains. We
prove that in the quantum case dimensions of the homogeneous components of the
graded vector spaces of k-forms are the same as in the classical case. This
result is well-known for quantum matrices.
The quadratic algebras, which we consider in the present paper, are
q-analogues of the polynomial algebras on prehomogeneous vector spaces of
commutative parabolic type. This enables us to prove that the de Rham complex
is isomorphic to the dual of a quantum analogue of the generalized
Bernstein-Gelfand-Gelfand resolution.Comment: LaTeX2e, 51 pages; changed conten
-Algebras, the BV Formalism, and Classical Fields
We summarise some of our recent works on -algebras and quasi-groups
with regard to higher principal bundles and their applications in twistor
theory and gauge theory. In particular, after a lightning review of
-algebras, we discuss their Maurer-Cartan theory and explain that any
classical field theory admitting an action can be reformulated in this context
with the help of the Batalin-Vilkovisky formalism. As examples, we explore
higher Chern-Simons theory and Yang-Mills theory. We also explain how these
ideas can be combined with those of twistor theory to formulate maximally
superconformal gauge theories in four and six dimensions by means of
-quasi-isomorphisms, and we propose a twistor space action.Comment: 19 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium
Higher Structures in M-Theory, August 201
Is there a Jordan geometry underlying quantum physics?
There have been several propositions for a geometric and essentially
non-linear formulation of quantum mechanics. From a purely mathematical point
of view, the point of view of Jordan algebra theory might give new strength to
such approaches: there is a ``Jordan geometry'' belonging to the Jordan part of
the algebra of observables, in the same way as Lie groups belong to the Lie
part. Both the Lie geometry and the Jordan geometry are well-adapted to
describe certain features of quantum theory. We concentrate here on the
mathematical description of the Jordan geometry and raise some questions
concerning possible relations with foundational issues of quantum theory.Comment: 30 page
The kernel of the edth operators on higher-genus spacelike two-surfaces
The dimension of the kernels of the edth and edth-prime operators on closed,
orientable spacelike 2-surfaces with arbitrary genus is calculated, and some of
its mathematical and physical consequences are discussed.Comment: 12 page
3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations
The equivalence problem for second order ODEs given modulo point
transformations is solved in full analogy with the equivalence problem of
nondegenerate 3-dimensional CR structures. This approach enables an analog of
the Feffereman metrics to be defined. The conformal class of these (split
signature) metrics is well defined by each point equivalence class of second
order ODEs. Its conformal curvature is interpreted in terms of the basic point
invariants of the corresponding class of ODEs
The influence of waves on morphodynamic impacts of energy extraction at a tidal stream turbine site in the Pentland Firth
Extraction of energy from tidal streams has the potential to impact on the morphodynamics of areas such as sub-tidal sandbanks via alteration of hydrodynamics. Marine sediment transport is forced by both wave and tidal currents. Past work on tidal stream turbine impacts has largely ignored the contribution of waves. Here, a fully coupled hydrodynamic, spectral wave and sediment transport model is used to assess the importance of including waves in simulations of turbine impact on seabed morphodynamics. Assessment of this is important due to the additional expense of including waves in simulations. Focus is given to a sandbank in the Inner Sound of the Pentland Firth. It is found that inclusion of wave action alters hydrodynamics, although extent of alteration is dependant of wave direction. Magnitude of sediment transport is increased when waves are included in the simulations and this has implications for morphological and volumetric changes. Volumetric changes are substantially increased when wave action is included: the impact of including waves is greater than the impact of including tidal stream turbines. Therefore it is recommended that at tidal turbine array sites exposed to large swell or wind-seas, waves should be considered for inclusion in simulations of physical impact
Large scale three-dimensional modelling for wave and tidal energy resource and environmental impact : methodologies for quantifying acceptable thresholds for sustainable exploitation
We describe a modelling project to estimate the potential effects of wave & tidal stream renewables on the marine environment. • Realistic generic devices to be used by those without access to the technical details available to developers are described. • Results show largely local sea bed effects at the level of the currently proposed renewables developments in our study area. • Large scale 3D modelling is critical to quantify the direct, indirect and cumulative effects of renewable energy extraction. • This is critical to comply with planning & environmental impact assessment regulations and achieve Good Environmental Status
Quantum Attractor Flows
Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as a
holographic correspondence in the mini-superspace approximation, we study the
radial quantization of stationary, spherically symmetric black holes in four
dimensions. A key ingredient is the classical equivalence between the radial
evolution equation and geodesic motion of a fiducial particle on the moduli
space M^*_3 of the three-dimensional theory after reduction along the time
direction. In the case of N=2 supergravity, M^*_3 is a para-quaternionic-Kahler
manifold; in this case, we show that BPS black holes correspond to a particular
class of geodesics which lift holomorphically to the twistor space Z of M^*_3,
and identify Z as the BPS phase space. We give a natural quantization of the
BPS phase space in terms of the sheaf cohomology of Z, and compute the exact
wave function of a BPS black hole with fixed electric and magnetic charges in
this framework. We comment on the relation to the topological string amplitude,
extensions to N>2 supergravity theories, and applications to automorphic black
hole partition functions.Comment: 43 pages, 6 figures; v2: typos and references added; v3: published
version, minor change
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