Related papers: Octonionic Realizations of 1-dimensional Extended …
Quaternionic and octonionic realizations of Clifford algebras and spinors are classified and explicitly constructed in terms of recursive formulas. The most general free dynamics in arbitrary signature space-times for both quaternionic and…
Quaternionic and octonionic spinors are introduced and their fundamental properties (such as the space-times supporting them) are reviewed. The conditions for the existence of their associated Dirac equations are analyzed. Quaternionic and…
The method of nonlinear realizations is applied for the conformally invariant description of the spinning particles in terms of geometrical quantities of the parameter spaces of the one dimensional N - extended superconformal groups. We…
The complete classification of the irreducible representations of the N-extended one-dimensional supersymmetry algebra linearly realized on a finite number of fields is presented. Off-shell invariant actions of one-dimensional…
In recent years, there is a growing interest in the studying octonions, which are 8-dimensional hypercomplex numbers forming the biggest normed division algebras over the real numbers. In particular, various tools of the classical complex…
It is shown that the supersymmetric quantum mechanics has an octonionic generalization. The generalization is based on the inclusion of quaternions into octonions. The elements from the coset octonions/quaternions are unobservables bacause…
In the first part of the talk I report on surprising relations between higher spin (HS) theory and nonlinear realizations of the supergroup OSp(1|8), a minimal superconformal extension of N=1, 4D supersymmetry with tensorial charges. The…
We give an octonionic formulation of the N = 1 supersymmetry algebra in D = 11, including all brane charges. We write this in terms of a novel outer product, which takes a pair of elements of the division algebra A and returns a real linear…
In this work we study the recently introduced octonionic duality for membranes. Restricting the self - duality equations to seven space dimensions, we provide various forms for them which exhibit the symmetries of the octonionic and…
Using octonions, more specifically, using a 4 x 4 matrix representation of octonions obtained with the help of algebraic properties of quaternions, we obtain the fully symmetric Maxwell's equations (Maxwell's equations with electric and…
The existence of maximally supersymmetric solutions to heterotic string theory that are not toroidal compactifications of the ten-dimensional superstring is established. We construct an exact fermionic realization of an N=1 supersymmetric…
In this paper some properties of the irreducible multiplets of representation for the N = (p, q) - extended supersymmetry in one dimension are discussed. Essentially two results are here presented. At first a peculiar property of the one…
We give a one dimensional octonionic representation of the different Clifford algebra Cliff(5,5)\sim Cliff(9,1), Cliff(6,6)\sim Cliff(10,2) and lastly Cliff(7,6)\sim Cliff(10,3) which can be given by (8x8) real matrices taking into account…
The theory of representations of Clifford algebras is extended to employ the division algebra of the octonions or Cayley numbers. In particular, questions that arise from the non-associativity and non-commutativity of this division algebra…
Various problems of mathematical physics consider octonions and split-octonions as a mathematical structure, which underpins the eight-dimensional nature of these problems. Therefore, it is not surprising that octonionic analysis has become…
The division algebras R, C, H, O are used to construct and analyze the N=1,2,4,8 supersymmetric extensions of the KdV hamiltonian equation. In particular a global N=8 super-KdV system is introduced and shown to admit a Poisson bracket…
We define a special matrix multiplication among a special subset of $2N\x 2N$ matrices, and study the resulting (non-associative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative…
String theory contains various extended objects. Among those, objects of codimension two (such as the D7-brane) are particularly interesting. Codimension two objects carry non-Abelian charges which are elements of a discrete U-duality group…
An explicit construction of theories of spinning particles, both massive and massless, is given with arbitrary extended supersymmetry on the world-line. As an application of our results, we give a universal description of 3D (and via…
One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed…