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Wednesday, March 8, 2017

Inscapes

Filed under: General,Geometry — Tags: — m759 @ 6:42 pm

"The particulars of attention,
whether subjective or objective,
are unshackled through form,
and offered as a relational matrix …."

— Kent Johnson in a 1993 essay

Illustration —

Commentary —

The 16 Dirac matrices form six anticommuting sets of five matrices each (Arfken 1985, p. 214):

1. alpha_1, alpha_2, alpha_3, alpha_4, alpha_5,

2. y_1, y_2, y_3, y_4, y_5,

3. delta_1, delta_2, delta_3, rho_1, rho_2,

4. alpha_1, y_1, delta_1, sigma_2, sigma_3,

5. alpha_2, y_2, delta_2, sigma_1, sigma_3,

6. alpha_3, y_3, delta_3, sigma_1, sigma_2.

SEE ALSO:  Pauli Matrices

REFERENCES:

Arfken, G. Mathematical Methods for Physicists, 3rd ed.  Orlando, FL: Academic Press, pp. 211-217, 1985.

Berestetskii, V. B.; Lifshitz, E. M.; and Pitaevskii, L. P. "Algebra of Dirac Matrices." §22 in Quantum Electrodynamics, 2nd ed.  Oxford, England: Pergamon Press, pp. 80-84, 1982.

Bethe, H. A. and Salpeter, E. Quantum Mechanics of One- and Two-Electron Atoms.  New York: Plenum, pp. 47-48, 1977.

Bjorken, J. D. and Drell, S. D. Relativistic Quantum Mechanics.  New York: McGraw-Hill, 1964.

Dirac, P. A. M. Principles of Quantum Mechanics, 4th ed.  Oxford, England: Oxford University Press, 1982.

Goldstein, H. Classical Mechanics, 2nd ed.  Reading, MA: Addison-Wesley, p. 580, 1980.

Good, R. H. Jr. "Properties of Dirac Matrices." Rev. Mod. Phys. 27, 187-211, 1955.

Referenced on Wolfram|Alpha:  Dirac Matrices

CITE THIS AS:

Weisstein, Eric W.  "Dirac Matrices."

From MathWorld— A Wolfram Web Resource. 
http://mathworld.wolfram.com/DiracMatrices.html

The Matrix Hypothesis

Filed under: General — Tags: , — m759 @ 9:20 am

"And so both of these bizarre events put one in mind of
a simple but arresting thesis: that we are  living in the Matrix,
and something has gone wrong with the controllers. . . .
The people or machines or aliens who are supposed to be
running our lives are having some kind of breakdown.
There’s a glitch, and we are in it.

Once this insight is offered, it must be said, everything  else
begins to fall in order."

— Adam Gopnik in The New Yorker , Feb. 27, 2017 

More recently …

Tuesday, November 22, 2016

Jargon

Filed under: General,Geometry — Tags: , , , — m759 @ 4:00 pm

See "sacerdotal jargon" in this journal.

For those who prefer scientific  jargon —

"… open its reading to
combinational possibilities
outside its larger narrative flow.
The particulars of attention,
whether subjective or objective,
are unshackled through form,
and offered as a relational matrix …."

— Kent Johnson in a 1993 essay

For some science that is not just jargon, see …

and, also from posts tagged Dirac and Geometry …

Anticommuting Dirac matrices as spreads of projective lines

The above line complex also illustrates an outer automorphism
of the symmetric group S6. See last Thursday's post "Rotman and
the Outer Automorphism."

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