• Corpus ID: 14889683

The Majorana spinor representation of the Poincare group

@article{Pedro2013TheMS,
  title={The Majorana spinor representation of the Poincare group},
  author={Leonardo Pedro},
  journal={arXiv: Mathematical Physics},
  year={2013}
}
  • L. Pedro
  • Published 1 May 2013
  • Mathematics, Physics
  • arXiv: Mathematical Physics
There are Poincare group representations on complex Hilbert spaces, like the Dirac spinor field, or real Hilbert spaces, like the electromagnetic field tensor. The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor field is a space-time dependent Majorana spinor, solution of the free Dirac equation. The Majorana-Fourier and Majorana-Hankel transforms of Majorana spinor fields are defined and related to the linear and angular momenta of a spin one-half… 
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References

SHOWING 1-10 OF 40 REFERENCES

Unitary representations of the Poincaré group and relativistic wave equations

This book is devoted to an extensive and systematic study on unitary representations of the Poincare group. The Poincare group plays an important role in understanding the relativistic picture of…

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

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…

Unitary Representations of the inhomogeneous Lorentz Group and their Significance in Quantum Physics

In honor of Minkowski's great contribution to Special Relativity, celebrated at this conference, we first review Wigner's theory of the projective irreducible representations of the inhomogeneous…

Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry

Quantum mechanics on a real Hilbert space

The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible…

Gauge Gravity and Electroweak Theory

Reformulation of the Dirac equation in terms of the real Spacetime Algebra (STA) reveals hidden geometric structure, including a geometric role for the unit imaginary as generator of rotations in a…

Clifford algebras, Fourier transforms and quantum mechanics

In this review, an overview is given of several recent generalizations of the Fourier transform, related to either the Lie algebra sl_2 or the Lie superalgebra osp(1|2). In the former case, one…

Clifford Algebras and Spinors

A historical review of spinors is given together with a construction of spinor spaces as minimal left ideals of Clifford algebras. Spinor spaces of euclidean spaces over reals have a natural linear…

Dirac, Majorana, and Weyl fermions

We discuss the Dirac, Majorana, and Weyl fermion fields. The definitions and motivations for introducing each kind of field is discussed, along with the connections between them. It is pointed out…

REAL SPINOR FIELDS.

The Dirac equation is expressed entirely in terms of geometrical quantities by providing a geometrical interpretation for the (−1)½ which appears explicitly in the Dirac equation. In the modification…