# Clifford Algebras in Physics

@article{Traubenberg2005CliffordAI, title={Clifford Algebras in Physics}, author={Michel Rausch de Traubenberg}, journal={Advances in Applied Clifford Algebras}, year={2005}, volume={19}, pages={869-908} }

Abstract.We study briefly some properties of real Clifford algebras and identify them as matrix algebras. We then show that the representation space on which Clifford algebras act are spinors and we study in details matrix representations. The precise structure of these matrices gives rise to the type of spinors one is able to construct in a given space-time dimension: Majorana or Weyl. Properties of spinors are also studied. We finally show how Clifford algebras enable us to construct…

## 31 Citations

Some Results on Cubic and Higher Order Extensions of the Poincare Algebra

- Mathematics
- 2008

In these lectures we study some possible higher order (of degree greater than two) extensions of the Poincare algebra. We first give some general properties of Lie superalgebras with some emphasis on…

Spinorial Geometry and Supergravity

- Physics
- 2006

In the main part of this thesis, we present the foundations and initial results of the Spinorial Geometry formalism for solving Killing spinor equations. This method can be used for any supergravity…

Clifford algebras and their applications to Lie groups and spinors

- Mathematics
- 2017

In these lectures, we discuss some well-known facts about Clifford algebras: matrix representations, Cartan's periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in…

Pauli theorem in the description of n-dimensional spinors in the Clifford algebra formalism

- Mathematics
- 2013

We discuss a generalized Pauli theorem and its possible applications for describing n-dimensional (Dirac, Weyl, Majorana, and Majorana-Weyl) spinors in the Clifford algebra formalism. We give the…

Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime

- Physics
- 2005

A theory in which 4-dimensional spacetime is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of…

Dark matter and localised fermions from spherical orbifolds?

- Physics
- 2016

A bstractWe study a class of six-dimensional models based on positive curvature surfaces (spherical 2-orbifolds) as extra-spaces. Using the Newman-Penrose formalism, we discuss the particle spectrum…

ec 2 00 6 Fermions in three-dimensional spinfoam quantum gravity

- Physics
- 2008

We study the coupling of massive fermions to the quantum mechanical dynamics of spacetime emerging from the spinfoam approach in three dimensions. We first recall the classical theory before…

Dual Hyperquaternion Poincaré Groups

- Mathematics
- 2021

A new representation of the Poincare groups in n dimensions via dual hyperquaternions is developed, hyperquaternions being defined as a tensor product of quaternion algebras (or a subalgebra…

Fermions in three-dimensional spinfoam quantum gravity

- Physics
- 2007

We study the coupling of massive fermions to the quantum mechanical dynamics of spacetime emerging from the spinfoam approach in three dimensions. We first recall the classical theory before…

Spin and Clifford Algebras, an Introduction

- Mathematics
- 2009

Abstract.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…

## References

SHOWING 1-10 OF 19 REFERENCES

Supergravity, Brane Dynamics and String Duality

- Mathematics
- 1998

In this review we show that a Clifford algebra possesses a unique irreducible representation; the spinor representation. We discuss what types of spinors can exist in Minkowski space-times and we…

All Possible Symmetries of the S Matrix

- Mathematics
- 1967

We prove a new theorem on the impossibility of combining space-time and internal symmetries in any but a trivial way. The theorem is an improvement on known results in that it is applicable to…

Supersymmetry and Supergravity

- Physics
- 1992

The first edition of this book appeared in 1983 and was based on a series of lectures given at Princeton in 1983 by Julius Wess. Since the appearance of the first edition much work has been done on…

On Unitary Representations of the Inhomogeneous Lorentz Group

- Physics
- 1939

It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally…

Introduction to Supersymmetry: Cambridge Monographs on Mathematical Physics

- Physics
- 1987

Peter G 0 Freund 1986 Cambridge: Cambridge University Press x + 152 pp price £20 ISBN 0 521 26880X The success of gauge theories as a solution to the problem of interacting relativistic quantum…

String theory.

- PhysicsProceedings of the National Academy of Sciences of the United States of America
- 1998

The current “standard model” of particle physics—which is nearly 25 years old, has much experimental evidence in its favor and is comprised of six quarks, six leptons, four forces, and the as yet unobserved Higgs boson—contains internal indications that it, too, may be just another step along the path toward uncovering the truly fundamental degrees of freedom.

The Quantum Theory of the Electron. Part II

- Physics
- 1928

In a previous paper by the author* it is shown that the general theory of quantum mechanics together with relativity require the wave equation for an electron moving in an arbitrary electromagnetic…