Structure
The spacetime algebra is built up from combinations of one time-like basis vector and three orthogonal space-like vectors, under the multiplication rule
where is the Minkowski metric with signature (+ − − −)
Thus, otherwise .
The basis vectors share these properties with the Dirac matrices, but no explicit matrix representation is utilized in STA.
This generates a basis of one scalar, four vectors, six bivectors, four pseudovectors and one pseudoscalar .
Read more about this topic: Spacetime Algebra
Famous quotes containing the word structure:
“A structure becomes architectural, and not sculptural, when its elements no longer have their justification in nature.”
—Guillaume Apollinaire (1880–1918)
“For the structure that we raise,
Time is with materials filled;
Our to-days and yesterdays
Are the blocks with which we build.”
—Henry Wadsworth Longfellow (1809–1882)
“If rightly made, a boat would be a sort of amphibious animal, a creature of two elements, related by one half its structure to some swift and shapely fish, and by the other to some strong-winged and graceful bird.”
—Henry David Thoreau (1817–1862)