相关论文: Clifford algebras, spinors and fundamental interac…

Double coverings of the orthogonal groups of the real and complex spaces are considered. The relation between discrete transformations of these spaces and fundamental automorphisms of Clifford algebras is established, where an isomorphism…

This is the first monograph on the geometry of anisotropic spinor spaces and its applications in modern physics. The main subjects are the theory of gravity and matter fields in spaces provided with off--diagonal metrics and associated…

We show that Clifford algebras provide a natural language to describe the physics of liquid crystal defects in 3D. This framework shows that most of these defects have fermionic nature, as the director field profile on a 2D cross section…

We further explore the idea that physics takes place in Clifford space which should be considered as a generalization of spacetime. Following the old observation that spinors can be represented as members of left ideals of Clifford algebra,…

By bridging geometric and algebraic concepts, this dissertation lays the groundwork for a comprehensive study of the Clifford structures on bundles and spinor fields. We delve into the K\"ahler-Atiyah bundle, which encapsulates the essence…

A concrete representation of the Clifford algebra (for any hyperbolic quadratic space) is given using what are called Suslin matrices. This explicit construction is used to analyze the corresponding Spin groups and the involution and might…

Spinors are central to physics: all matter (fermions) is made of spinors, and all forces arise from symmetries of spinors. It is common to consider the geometric (Clifford) algebra as the fundamental edifice from which spinors emerge. This…

We show that the space of Euclid's parameters for Pythagorean triples is endowed with a natural symplectic structure and that it emerges as a spinor space of the Clifford algebra $\mathbb{R}_{2,1}$, whose minimal version may be…

Because of the isomorphism ${C \kern -0.1em \ell}_{1,3}(\Bbb{C})\cong{C \kern -0.1em \ell}_{2,3}(\Bbb{R})$, it is possible to complexify the spacetime Clifford algebra ${C \kern -0.1em \ell}_{1,3}(\Bbb{R})$ by adding one additional timelike…

The representations of Clifford algebras and their involutions and anti-involutions are fully investigated since decades. However, these representations do sometimes not comply with usual conventions within physics. A few simple examples…

This paper surveys the application of geometric algebra to the physics of electrons. It first appeared in 1996 and is reproduced here with only minor modifications. Subjects covered include non-relativistic and relativistic spinors, the…

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…

In this paper we find a Clifford algebra associated to generalized Fibonacci quaternions. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice-versa.

We introduce spinors, at a level appropriate for an undergraduate or first year graduate course on relativity, astrophysics or particle physics. The treatment assumes very little mathematical knowledge (mainly just vector analysis and some…

The first time that the connection between isometric immersion of surfaces and solutions of the Dirac equation appeared in the literature was in the seminal paper of Thomas Friedrich in 1998. In consequence of that, several authors…

Division algebras have demonstrated their utility in studying non-associative algebras and their connection to the Standard Model through complex Clifford algebras. This article focuses on exploring the connection between these complex…

The equations defining pure spinors are interpreted as equations of motion formulated on the lightcone of a ten-dimensional, lorentzian, momentum space. Most of the equations for fermion multiplets, usually adopted by particle physics, are…

We investigate a model in which spinors are considered as being embedded within the Clifford algebra that operates on them. In Minkowski space $M_{1,3}$, we have four independent 4-component spinors, each living in a different minimal left…

We study holonomy algebras generated by an algebraic element of the Clifford algebra, or equivalently, the holonomy algebras of certain spin connections in flat space. We provide series of examples in arbitrary dimensions and establish…

I apply the algebraic framework introduced in arXiv:1101.4542v3[math.MG] to Minkowski (pseudo-Euclidean) spaces in 2, 3, and 4 dimensions. The exposition follows the template established in arXiv:1307.2917[math.MG] for Euclidean spaces. The…