Dirac Equation In The Algebra Of Physical Space
The Dirac equation, as the relativistic equation that describes spin 1/2 particles in quantum mechanics can be written in terms of the Algebra of physical space (APS), which is a case of a Clifford algebra or geometric algebra that is based in the use of paravectors.
The Dirac equation in APS, including the electromagnetic interaction, reads
Another form of the Dirac equation in terms of the Space time algebra was given earlier by David Hestenes.
In general, the Dirac equation in the formalism of geometric algebra has the advantage of providing a direct geometric interpretation.
Read more about Dirac Equation In The Algebra Of Physical Space: Relation With The Standard Form, Electromagnetic Gauge, Current, Second Order Dirac Equation, Dirac Lagrangian
Famous quotes containing the words equation, algebra, physical and/or space:
“A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”
—Norman Mailer (b. 1923)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)
“Not too many years ago, a child’s experience was limited by how far he or she could ride a bicycle or by the physical boundaries that parents set. Today ... the real boundaries of a child’s life are set more by the number of available cable channels and videotapes, by the simulated reality of videogames, by the number of megabytes of memory in the home computer. Now kids can go anywhere, as long as they stay inside the electronic bubble.”
—Richard Louv (20th century)
“In bourgeois society, the French and the industrial revolution transformed the authorization of political space. The political revolution put an end to the formalized hierarchy of the ancien regimé.... Concurrently, the industrial revolution subverted the social hierarchy upon which the old political space was based. It transformed the experience of society from one of vertical hierarchy to one of horizontal class stratification.”
—Donald M. Lowe, U.S. historian, educator. History of Bourgeois Perception, ch. 4, University of Chicago Press (1982)