imaginary Lie vs real Hadamard groups

[AntonioLao]

The search continues for a symmetric gauge group that can completely describe a quantum field theory of gravity. The study of continuous groups (e.g. rotation groups) was started by Sophus Lie (1842-99) in the latter parts of the 1800s. He sought to characterize geometries in which rigid body motions are possible. But he analyzed the same problem stated by Helmholtz earlier that if the motions of rigid bodies are to be possible on a space then Riemann’s expression for ds in a space of constant curvature is the only one possible. The result of his research became known as a theory of continuous transformation groups. He then characterized the spaces in which rigid motions are possible by means of the kinds of groups of transformations which these spaces permit. However, where and when these spaces are replaced by a spacetime continuum, the results at best can only be imaginary Lie groups, for examples, Pauli spin matrices and Dirac matrices in QM.

To return to the real continuous groups, it is possible simply by using square symmetric Hadamard matrices. Whose elements are either 1 or -1. Abelian additions give complete descriptions of all physical charges: electric, weak, and color. Abelian multiplications give complete descriptions of physical masses beginning from first principle. The spacetime projections of these groups are completely described by parametric equations for an alpha and a beta angular parameter. Whose inverse domains are found within a sieve of Diophantus. Furthermore, the alpha domain or the beta domain does not simultaneously exist thus giving a true real quantized nature of the spacetime continuum.

[mkirkpatrick]

All things exist within the mind,however "allthings" are not
particulary real,at best they are only relatively real,thereby
not absolute.



regards michael.

[AntonioLao]

Are then the imaginaries to be found in the imagine nation?

[mkirkpatrick]

Are then the imaginaries to be found in the imagine nation?

Yes there are!



regards michael.

[AntonioLao]

But some are busily giving us the electric promotion?

[mkirkpatrick]

But some are busily giving us the electric promotion?

Then the sparks will fly!




regards michael.

[AntonioLao]

Also periodic Fourier transformations.

[mkirkpatrick]

Also periodic Fourier transformations.

Them as well of course!




regards michael.

[AntonioLao]

But Fourier never wanted to use imaginary numbers and I'm not sure who started it.

[mkirkpatrick]

But Fourier never wanted to use imaginary numbers and I'm not sure who started it.

Well then we can start by refusing to use them here.



regards michael.