Related papers: Clifford Parallelisms and External Planes to the K…

We study the geometry of spaces of planes on smooth complete intersections of three quadrics, with a view toward rationality questions.

Systems of equations are invariant under "polydimensional transformations" which reshuffle the geometry such that what is a line or a plane is dependent upon the frame of reference. This leads us to propose an extension of Clifford calculus…

Principle of ``Superrelativity'' has been proposed in order to avoid the contradiction between principle of relativity and foundations of quantum theory. Solutions of a newly derived non-linear Klein-Gordon equation presumably may be…

We discuss how transformations in a three dimensional euclidean space can be described in terms of the Clifford algebra $\mathcal{C}\ell_{3,3}$ of the quadratic space $\mathbb{R}^{3,3}$. We show that this algebra describes in a unified way…

Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. Let $End(V)$ denote the $K$-algebra consisting of all $K$-linear transformations from $V$ to $V$. We consider a pair $A,A^* \in End(V)$ that…

The projective variety of square-zero elements in the six-dimensional minimal supersymmetry algebra is isomorphic to $\mathbb{P}^1 \times \mathbb{P}^3$. We use this fact, together with the pure spinor superfield formalism, to study…

A global vector field $v$ on a "spacetime" differentiable manifold $\mathrm{V}$, of dimension $N+1$, defines a congruence of world lines: the maximal integral curves of $v$, or orbits. The associated global space $\mathrm{N}\_v$ is the set…

We give a geometric approach to the relation between the irreducible components of the characteristic varieties of local systems on a plane curve arrangement complement and the associated pencils of plane curves discovered recently by M.…

We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…

We introduce the notion of even Clifford structures on Riemannian manifolds, a framework generalizing almost Hermitian and quaternion-Hermitian geometries. We give the complete classification of manifolds carrying parallel even Clifford…

We introduce the notion of a field of covariances, a contravariant functor from non-commutative probability spaces to Hilbert spaces, as the natural categorical analogue of statistical covariance. In the case of finite-dimensional…

Using the method of covariant symbols we compute the divergent part of the effective action of the Proca field with non-minimal mass term. Specifically a quantum Abelian vector field with a non-derivative coupling to an external tensor…

We investigate the properties of the Extended Fock Basis (EFB) of Clifford algebras introduced in [1]. We show that a Clifford algebra can be seen as a direct sum of multiple spinor subspaces that are characterized as being left…

Let $V$ be a finite dimensional vector space over a field $F$ of characteristic different from 2, and let $Q$ be a nondegenerate, symmetric, bilinear form on $V$. Let $C\ell(V,Q)$ be the Clifford algebra determined by $V$ and $Q$. The…

We begin showing that for even dimensional vector spaces $V$ all automorphisms of their Clifford algebras are inner. So all orthogonal transformations of $V$ are restrictions to $V$ of inner automorphisms of the algebra. Thus under…

The automorphism invariant theory of Crawford[J. Math. Phys. 35, 2701 (1994)] has show great promise, however its application is limited by the paradigm to the domain of spin space. Our conjecture is that there is a broader principle at…

We develop a theory of Prym varieties and cubic threefolds over fields of characteristic $2$. As an application, we prove that smooth cubic threefolds are non-rational over an arbitrary field and solve a conjecture of Deligne regarding…

We give an expanded discussion of the proposal that spacetime supersymmetry representations may be viewed as having their origins in 1D theories that involve a special class of real Clifford algebras. These 1D theories reproduce the…

We study plane algebraic curves defined over a field k of arbitrary characteristic as coverings of the the projective line and the problem of enumerating branched coverings of $\mathbb{P}^{1}$ by using combinatorial methods.

We have generalized the well-known statement that the Clifford group is a unitary 3-design into symmetric cases by extending the notion of unitary design. Concretely, we have proven that a symmetric Clifford group is a symmetric unitary…