What is geometric algebra used for?
Geometric algebra allows more than vectors and matrices to represent objects and operators. It has a ‘span’ (outer) product, which makes general subspaces elements of computation. It has an invertible `geometric product’, which allows you to divide by subspaces.
Who made geometric algebra?
William Clifford
It defines a product that’s strongly motivated by geometry and can be taken between any two objects. For example, the product of two vectors taken in a certain way represents their common plane. This system was invented by William Clifford and is more commonly known as Clifford algebra.
What is modern twistor theory?
In theoretical physics, twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a branch of theoretical and mathematical physics. Penrose proposed that twistor space should be the basic arena for physics from which space-time itself should emerge.
How do tornadoes work physics?
This rotation is caused by wind shear. When this rotating air is drawn into the updraft, it becomes tilted vertically. “The updraft lifts the rotating cylinder within the supercell. The rotating cylinder of air narrows, becoming stretched, and spins faster and faster forming a tornado,“ NOAA said.
Are quaternions spinors?
of quaternions, as in the case of two dimensions the only representation of the algebra of even-graded elements is on itself. Thus the (real) spinors in three-dimensions are quaternions, and the action of an even-graded element on a spinor is given by ordinary quaternionic multiplication.
What is the twistor theory in physics?
From Wikipedia, the free encyclopedia In theoretical physics, twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a branch of theoretical and mathematical physics. Penrose proposed that twistor space should be the basic arena for physics from which space-time itself should emerge.
Why is twistor geometry chiral?
The chiral nature of twistor geometry fits naturally with a long tradition going back to Plebanski and Ashtekar of formulating gravity theories using just the self-dual part of the spin connection. For a recent discussion of the sort of gravity theory that appears naturally here, see Kirill Krasnov’s Self-Dual Gravity.
What is conformal invariance in twistor geometry?
In twistor geometry, conformal invariance is a basic property, realized in a simple way, by the linear S L ( 4, C) group action on the twistor space C 4. This is a complex group action with real forms S U ( 2, 2) (Minkowski) and S L ( 2, H) (Euclidean). The electroweak S U ( 2) is inherently chiral.
What is Twistorial formulae?
Twistorial formulae for interactions beyond the self-dual sector first arose from Witten’s twistor string theory. This is a quantum theory of holomorphic maps of a Riemann surface into twistor space.