Word info

Clifford algebra

Noun

Meaning

Clifford algebra (plural Clifford algebras)

(algebra, mathematical physics) A unital associative algebra which generalizes the algebra of quaternions but which is not necessarily a division algebra; it is generated by a set of




γ

i




{\displaystyle \gamma _{i}}

(with i ranging from, say, 1 to n) such that the square of each




γ

i




{\displaystyle \gamma _{i}}

is fixed to be either +1 or −1, depending on each i, and such that any product




γ

i



γ

j




{\displaystyle \gamma _{i}\gamma _{j}}

anticommutes when its factors are distinct (i.e., when



i

j


{\displaystyle i\neq j}

).

Source: en.wiktionary.org

Examples

Eddington believed he had identified an algebraic basis for fundamental physics, which he termed "E-numbers" (representing a certain group – a Clifford algebra ). Source: Internet

Component spinors Given a vector space V and a quadratic form g an explicit matrix representation of the Clifford algebra Cℓ(V, g) can be defined as follows. Source: Internet

In this way, the spinor representations are identified with certain subspaces of the Clifford algebra itself. Source: Internet

Geometric algebra is distinguished from Clifford algebra in general by its restriction to real numbers and its emphasis on its geometric interpretation and physical applications. Source: Internet

In 1999 he showed how Einstein's equations of general relativity could be formulated within a Clifford algebra that is directly linked to quaternions. Source: Internet

Namely, the norm operation in a certain type of algebraic system (now known as a Clifford algebra ). Source: Internet

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