相关论文: How to generate families of spinors

We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z_2^n by a cocycle. Our approach is more general than the usual…

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…

We are proposing a new way of describing families of quarks and leptons, using the approach unifying all the internal degrees of freedom, proposed by one of us. Spinors, living in d(=1+13)-dimensional space, carry in this approach only the…

We suggest Clifford algebra as a useful simplifying language for present quantum dynamics. Clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups. Aggregates using…

Representations of Spin groups and Clifford algebras derived from the structure of qubit trees are introduced in this work. For ternary trees the construction is more general and reduction to binary trees is formally defined by deletion of…

The relationship between spinors and Clifford (or geometric) algebra has long been studied, but little consistency may be found between the various approaches. However, when spinors are defined to be elements of the even subalgebra of some…

The internal degrees of freedom of fermions are in the spin-charge-family theory described by the Clifford algebra objects, which are superposition of an odd number of $\gamma^a$'s. Arranged into irreducible representations of…

Clifford algebras are used for definition of spinors. Because of using spin-1/2 systems as an adequate model of quantum bit, a relation of the algebras with quantum information science has physical reasons. But there are simple mathematical…

We use our Clifford algebra technique, that is nilpotents and projectors which are binomials of the Clifford algebra objects $\gamma^a$ with the property $\{\gamma^a,\gamma^b\}_+ = 2 \eta^{ab}$, for representing quantum gates and quantum…

The modern algebra concepts are used to construct tables of algebraic spinors related to Clifford algebra multivectors with real and complex coefficients. The following data computed by Mathematica are presented in form of tables for…

In this work, we propose a novel framework for defining the dual structure of a spinor. This construction relies on the basis elements of the Clifford algebra, leading to a covariant structure that embeds the dual. The formulation includes…

Prompted by a recent demonstration that the structure of a single quark-lepton generation may be understood via a Dirac-like linearization of the form p^2+x^2, we analyze the corresponding Clifford algebra in some detail. After classifying…

We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method for analyzing of commutators and anticommutators of Clifford algebra…

In this short pedagogical presentation, we introduce the spin groups and the spinors from the point of view of group theory. We also present, independently, the construction of the low dimensional Clifford algebras. And we establish the…

In this work we explore the structure of Clifford algebras and the representations of the algebraic spinors in quantum information theory. Initially we present an general formulation through elements of left minimal ideals in tensor…

We give an algebraic formulation based on Clifford algebras and algebraic spinors for quantum information. In this context, logic gates and concepts such as chirality, charge conjugation, parity and time reversal are introduced and explored…

These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…

It is shown that since the geometric spinors are elements of Clifford algebras, they must have the same transformation properties as any other Clifford number. In general, a Clifford number $\Phi$ transforms into a new Clifford number…

The approach unifying all the internal degrees of freedom - proposed by one of us - is offering a new way of understanding families of quarks and leptons. Spinors, namely, living in d(=1+13)-dimensional space, manifest in the observed…

In this paper, we make the case that Clifford algebra is the natural framework for root systems and reflection groups, as well as related groups such as the conformal and modular groups: The metric that exists on these spaces can always be…