Search results
Results from the WOW.Com Content Network
Examples of geometric algebras applied in physics include the spacetime algebra (and the less common algebra of physical space) and the conformal geometric algebra. Geometric calculus , an extension of GA that incorporates differentiation and integration , can be used to formulate other theories such as complex analysis and differential ...
The name paravector is used for the combination of a scalar and a vector in any Clifford algebra, known as geometric algebra among physicists.. This name was given by J. G. Maks in a doctoral dissertation at Technische Universiteit Delft, Netherlands, in 1989.
Chris J. L. Doran is a physicist, Director of Studies in Natural Sciences for Sidney Sussex College, Cambridge. He founded Geomerics, and is its Chief Operating Officer. Doran obtained his Ph.D. in 1994 on the topic of Geometric Algebra and its Application to Mathematical Physics. He was an EPSRC Advanced Fellow from 1999 to 2004.
In mathematical physics, spacetime algebra (STA) is the application of Clifford algebra Cl 1,3 (R), or equivalently the geometric algebra G(M 4) to physics. Spacetime algebra provides a "unified, coordinate-free formulation for all of relativistic physics, including the Dirac equation, Maxwell equation and General Relativity" and "reduces the mathematical divide between classical, quantum and ...
In physics, the algebra of physical space (APS) is the use of the Clifford or geometric algebra Cl 3,0 (R) of the three-dimensional Euclidean space as a model for (3+1)-dimensional spacetime, representing a point in spacetime via a paravector (3-dimensional vector plus a 1-dimensional scalar).
David Orlin Hestenes (born May 21, 1933) is a theoretical physicist and science educator. He is best known as chief architect of geometric algebra as a unified language for mathematics and physics, [1] and as founder of Modelling Instruction, a research-based program to reform K–12 Science, Technology, Engineering, and Mathematics (STEM) education.
The operations of geometric algebra have the effect of mirroring, rotating, translating, and mapping the geometric objects that are being modelled to new positions. Clifford algebras in general and geometric algebra in particular have been of ever increasing importance to mathematical physics, [1] geometry, [2] and computing. [3]
The universal geometric algebra (n, n) of order 2 2n is defined as the Clifford algebra of 2n-dimensional pseudo-Euclidean space R n, n. [1] This algebra is also called the "mother algebra". It has a nondegenerate signature. The vectors in this space generate the algebra through the geometric product.