Related papers: An Introduction to Clifford Supermodules

Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. But the spin group is not the only subgroup of the Clifford algebra. An algebraist's perspective on…

The Proca field describes a massive relativistic spin-$1$ particle and was originally formulated in Minkowski spacetime. Here we consider a variety of generalizations in globally hyperbolic spacetimes, including couplings between a number…

We study the dynamics of multiwormhole configurations within the framework of the Euclidean Polyakov approach to string theory, incorporating a modification to the Hamiltonian which leads to a Planckian probability measure for the Coleman…

We use geometric parabolic induction functors and the adjoint functors for the supergroups Osp(2m+1,2n) (where m and n vary) to categorify the action of the infinite-dimensional Clifford algebra on the Fock space of semi-infinite forms.

An alternative, pedagogically simpler derivation of the allowed physical wave fronts of a propagating electromagnetic signal is presented using geometric algebra. Maxwell's equations can be expressed in a single multivector equation using…

In this paper we develop the Hermitian refinement of symplectic Clifford analysis, by introducing a complex structure $\mathbb{J}$ on the canonical symplectic manifold $(\mathbb {R}^{2n},\omega_0)$. This gives rise to two symplectic Dirac…

A generalization of the term "generalized Clifford algebras" (as appears in papers on advances in applied Clifford algebras) is introduced. This algebra is studied by means of structure theory of central simple algebras. A graph theoretical…

Real and complex Clifford bundles and Dirac operators defined on them are considered. By using the index theorems of Dirac operators, table of topological invariants is constructed from the Clifford chessboard. Through the relations between…

We re-consider the procedure of ``taking a square root of the Dirac equation'' on the superspace and show that it leads to the well known superfield W_\alpha and to the proper equations of motion for the components, i.e. the Maxwell…

The tensor product of the division algebras, which is a kernel for the structure of the Standard Model, is also a root for the Clifford algebra of (1,9)-space-time. A conventional Dirac Lagrangian, employing the (1,9)-Dirac operator acting…

The semiclassical kinetic theory of Dirac particles in the presence of external electromagnetic fields and global rotation is established. To provide the Hamiltonian formulation of Dirac particles a symplectic two-form which is a matrix in…

We survey results on compact Clifford-Klein forms of homogeneous spaces, with a focus on recent contributions and organized around approaches via topology, geometry and dynamics. In addition, we survey results on moduli spaces of compact…

Clifford geometric algebras of multivectors are treated in detail. These algebras are build over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear, that…

Classes of relativistic symmetries accommodating supersymmetric patterns are considered for the Dirac Hamiltonian with axially-deformed scalar and vector potentials.

In this paper the conformal Dirac operator on the sphere is defined to be operating on the space of square-integrable Clifford algebra-valued functions. The spinorial Laplacian of order d>0 is defined and used to establish Sobolev embedding…

Starting from the full group of symmetries of a system we select a discrete subset of transformations which allows to introduce the Clifford algebra of operators generating new supercharges of extended supersymmetry. The system defined by…

We consider a relativistic charged particle in a background scalar field depending on both space and time. Poincar\'e, dilation and special conformal symmetries of the field generate conserved quantities in the charge motion, and we exploit…

Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields,…

This paper contains a review of the theoretical foundations of Clifford algebras, spinors and spinor bundles in the so-called co-frame formalism. A compact index-free notation is introduced, along with a series of identities useful for…

We show that the binary representation of the integers has a role to play in many aspects of Clifford algebras.