44 research outputs found
EXTENDED SUPERCONFORMAL SYMMETRY, FREUDENTHAL TRIPLE SYSTEMS AND GAUGED WZW MODELS
We review the construction of extended ( N=2 and N=4 ) superconformal
algebras over triple systems and the gauged WZW models invariant under them.
The N=2 superconformal algebras (SCA) realized over Freudenthal triple systems
(FTS) admit extension to ``maximal'' N=4 SCA's with SU(2)XSU(2)XU(1) symmetry.
A detailed study of the construction and classification of N=2 and N=4 SCA's
over Freudenthal triple systems is given. We conclude with a study and
classification of gauged WZW models with N=4 superconformal symmetry.Comment: Invited talk presented at the Gursey Memorial Conference I in
Istanbul, Turkiye (June 6-10, 1994). To appear in the proceedings of the
conference. (21 pages. Latex document.
Fundamental representations and algebraic properties of biquaternions or complexified quaternions
The fundamental properties of biquaternions (complexified quaternions) are
presented including several different representations, some of them new, and
definitions of fundamental operations such as the scalar and vector parts,
conjugates, semi-norms, polar forms, and inner and outer products. The notation
is consistent throughout, even between representations, providing a clear
account of the many ways in which the component parts of a biquaternion may be
manipulated algebraically
Unified N=2 Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Four Dimensions
We study unified N=2 Maxwell-Einstein supergravity theories (MESGTs) and
unified Yang-Mills Einstein supergravity theories (YMESGTs) in four dimensions.
As their defining property, these theories admit the action of a global or
local symmetry group that is (i) simple, and (ii) acts irreducibly on all the
vector fields of the theory, including the ``graviphoton''. Restricting
ourselves to the theories that originate from five dimensions via dimensional
reduction, we find that the generic Jordan family of MESGTs with the scalar
manifolds [SU(1,1)/U(1)] X [SO(2,n)/SO(2)X SO(n)] are all unified in four
dimensions with the unifying global symmetry group SO(2,n). Of these theories
only one can be gauged so as to obtain a unified YMESGT with the gauge group
SO(2,1). Three of the four magical supergravity theories defined by simple
Euclidean Jordan algebras of degree 3 are unified MESGTs in four dimensions.
Two of these can furthermore be gauged so as to obtain 4D unified YMESGTs with
gauge groups SO(3,2) and SO(6,2), respectively. The generic non-Jordan family
and the theories whose scalar manifolds are homogeneous but not symmetric do
not lead to unified MESGTs in four dimensions. The three infinite families of
unified five-dimensional MESGTs defined by simple Lorentzian Jordan algebras,
whose scalar manifolds are non-homogeneous, do not lead directly to unified
MESGTs in four dimensions under dimensional reduction. However, since their
manifolds are non-homogeneous we are not able to completely rule out the
existence of symplectic sections in which these theories become unified in four
dimensions.Comment: 47 pages; latex fil
Filtering and Tracking with Trinion-Valued Adaptive Algorithms
A new model for three-dimensional processes based on the trinion algebra is introduced for the first time. Compared
with the pure quaternion model, the trinion model is more compact and computationally more efficient, while having similar or
comparable performance in terms of adaptive linear filtering. Moreover, the trinion model can effectively represent the general
relationship of state evolution in Kalman filtering, where the pure quaternion model fails. Simulations on real-world wind
recordings and synthetic data sets are provided to demonstrate the potentials of this new modeling method
Chirality and Symmetry Breaking in a discrete internal Space
In previous papers the permutation group S_4 has been suggested as an
ordering scheme for elementary particles, and the appearance of this finite
symmetry group was taken as indication for the existence of a discrete inner
symmetry space underlying elementary particle interactions. Here it is pointed
out that a more suitable choice than the tetrahedral group S_4 is the
pyritohedral group A_4 x Z_2 because its vibrational spectrum exhibits exactly
the mass multiplet structure of the 3 fermion generations. Furthermore it is
noted that the same structure can also be obtained from a primordial symmetry
breaking S_4 --> A_4. Since A_4 is a chiral group, while S_4 is achiral, an
argument can be given why the chirality of the inner pyritohedral symmetry
leads to parity violation of the weak interactions.Comment: 42 pages, 3 table
On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection
A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)