On a microscopic representation of space-time

@article{Dahm2011OnAM,
  title={On a microscopic representation of space-time},
  author={Rolf Dahm},
  journal={Physics of Atomic Nuclei},
  year={2011},
  volume={75},
  pages={1173-1181}
}
  • R. Dahm
  • Published 31 January 2011
  • Mathematics
  • Physics of Atomic Nuclei
We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low-energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of the operator actions. Then we discuss the geometrical origin of this noncompact Lie algebra and “reduce” the geometry in order to introduce in each of these steps coordinate definitions which can be related to an algebraic representation in terms of the… 

Figures from this paper

On a Microscopic Representation of Space-Time V
In order to extend our approach based on SU∗(4), we were led to (real) projective and (line) Complex geometry. So here we start from quadratic Complexe which yield naturally the ’light cone’ x 1 + x
On a Microscopic Representation of Space-Time III
  • R. Dahm
  • Mathematics
    Advances in Applied Clifford Algebras
  • 2019
Using the Dirac (Clifford) algebra $$\gamma ^{\mu }$$γμ as initial stage of our discussion, we summarize previous work with respect to the isomorphic 15 dimensional Lie algebra su*(4) as complex
The $C\ell(8)$ algebra of three fermion generations with spin and full internal symmetries
In this paper, the basis states of the minimal left ideals of the complex Clifford algebra $C\ell(8)$ are shown to contain three generations of Standard Model fermion states, with full Lorentzian,

References

SHOWING 1-10 OF 23 REFERENCES
A symmetry reduction scheme of the Dirac algebra without dimensional defects
In relating the Dirac algebra to homogeneous coordinates of a projective geometry, we present a simple geometric scheme which allows to identify various Lie algebras and Lie groups well-known from
On a microscopic representation of space–time IV
We summarize some previous work on SU(4) describing hadron representations and transformations as well as its noncompact “counterpart” SU*(4) being the complex embedding of SL(2,H). So after having
Quaternionic Projective Theory and Hadron Transformation Laws
A quaternionic projective theory based on the symmetry group Sl(2,H) allows one to identify various hadron models and many well-known particle transformation laws in its subgroup chains. Identifying
Relativistic SU(4) and Quaternions
A classification of hadrons and their interactions at low energies according to SU(4) allows to identify combinations of the fifteen mesons $\pi$, $\omega$ and $\rho$ within the spin-isospin
Differential Geometry, Lie Groups, and Symmetric Spaces
Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type Symmetric
XVII. On a new geometry of space
  • J. Plucker
  • Mathematics
    Philosophical Transactions of the Royal Society of London
  • 1865
I. On Linear Complexes of Right Lines. 1. Infinite space may be considered either as consisting of points or transversed by planes. The points, in the first conception, are determined by their
Relativistic Quantum Mechanics
In this text the authors develop a propagator theory of Dirac particles, photons, and Klein-Gordon mesons and per- form a series of calculations designed to illustrate various useful techniques and
Republication of: The geometry of free fall and light propagation
This is a reprinting of the paper by Jürgen Ehlers, Felix Pirani and Alfred Schild, first published in 1972 in a separate volume containing articles written in hounour of J. L. Synge. The original
Riemanns geometrische Ideen, ihre Auswirkung und ihre Verknüpfung mit der Gruppentheorie
I. Teil. Kontinuum.- 1. Begriff der n-dimensionalen Mannigfaltigkeit.- 2. Analysis situs.- 3. Einbettung und Uberlagerung.- II. Teil. Struktur.- 4. Das Strukturfeld (metrische, konforme, affine und
Groups and geometric analysis
Geometric Fourier analysis on spaces of constant curvature Integral geometry and Radon transforms Invariant differential operators Invariants and harmonic polynomials Spherical functions and
...
1
2
3
...