# Extended real Clifford - Dirac algebra and bosonic symmetries of the Dirac equation with nonzero mass

@article{Simulik2009ExtendedRC, title={Extended real Clifford - Dirac algebra and bosonic symmetries of the Dirac equation with nonzero mass}, author={Volodimir Simulik and Ivan Yu. Krivsky}, journal={arXiv: Mathematical Physics}, year={2009} }

The 64-dimensional extended real Clifford - Dirac (ERCD) algebra is introduced. On this basis the new pure matrix symmetries of the Dirac equation in Foldy - Wouthuysen representation are found: (i) the 32-dimensional A32 algebra, which is proved to be maximal pure matrix symmetry of this equation, (ii) two different realizations of the (1/2, 0)+(0, 1/2) representation of the S(1,3) algebra, (iii) reducible tensor-scalar (1, 0)+(0, 0) and irreducible vector (1/2,1/2) bosonic S(1,3)-symmetries…

## 4 Citations

APPLICATION OF THE GENERALIZED CLIFFORD-DIRAC ALGEBRA TO THE PROOF OF THE DIRAC EQUATION FERMI-BOSE DUALITY

- Physics
- 2013

The consideration of the bosonic properties of the Dirac equation with arbitrary mass has been continued. As the necessary mathematical tool the structure and different representations of the…

Fermi-Bose duality of the Dirac equation and extended real Clifford-Dirac algebra

- Physics
- 2010

We have proved on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass that this equation may describe not only fermions of spin 1/2 but also bosons of spin 1. The new…

On the Relativistic Canonical Quantum Mechanics and Field Theory of Arbitrary Spin

- Physics
- 2017

The new relativistic equations of motion for the particles with arbitrary spin and nonzero mass, suggested by author in years 2014–2016, are under consideration. The complete version of brief paper…

Extension of the Standard CD Algebra in the Axiomatic Approach for Spinor Field and Fermi–Bose Duality

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- 2017

The exclusive representations of the extended (29-dimensional) real-number Clifford–Dirac algebra are constructed for the spinor field. In the canonical Foldy–Wouthuysen representation for a…

## References

SHOWING 1-10 OF 47 REFERENCES

Bosonic symmetries of the Dirac equation

- Physics
- 2011

Abstract We have found on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass the new physically meaningful features of this equation. The new bosonic symmetries of…

Dirac equation and spin 1 representations, a connection with symmetries of the Maxwell equations

- Mathematics
- 1992

A unitary operator on the space of spinors that makes it possible to associate each transformation in this space with a transformation in the space of electromagnetic field strengths is found. A…

Symmetries of the complex Dirac-Kähler equation

- Mathematics
- 2005

AbstractWe consider a complex version of a Dirac-Kähler-type equation, the eight-component complex Dirac-Kähler equation with a nonvanishing mass, which can be decomposed into two Dirac equations by…

On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit

- Physics
- 1950

By a canonical transformation on the Dirac Hamiltonian for a free particle, a representation of the Dirac theory is obtained in which positive and negative energy states are separately represented by…

Clifford algebra in classical electrodynamical hydrogen atom model

- Physics
- 1997

AbstractA new model of the hydrogen atom spectrum description in the framework of classical electrodynamics, not quantum mechanics, is proposed. Zommerfeld formula for the fine structure of the…

On vector and pseudovector Lagrangians for electromagnetic field

- Physics
- 1989

SummaryA Lagrange function in terms of electromagnetic field strengths is constructed which is a 4-vector with respect to the total Poincaré group∼P(l, 3) and whose Euler-Lagrange equations are…

The Electron Theory

- MedicineNature
- 1913

The author leads his readers through the various phenomena associated with the Zeeman effect, Brownian movements, Lenard and Röntgen rays, up to the modern conceptions of the structure of the atom.

JR 旅客販売総合システム（マルス）における運用及び管理について

- Computer Science
- 1991

A dictionary definition of divisible number: a number is divisible by a number so that every digit of that number isdivisible by 3.

Symmetry in Physics

- Physics
- 1969

In this talk1 I shall take the liberty to confine myself to purely subjective ideas. In keeping with the spirit of the Symposium, I will not enter into technical details of any kind. By the same…