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sjhanjee
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Can matrix representations of any higher order Clifford Alebras be found ?
sjhanjee said:Thanks for the reply. Can you elaborate the even order case. I think you are using pauli matrices but I know only 3 of them. Can you clarify? Or can you tell me where to look for them.
sjhanjee said:Another question? My clifford algebras are Cl(0,n) (of negative signature) , not the space time algebra, so all the gamma matrices should square to -1.
sjhanjee said:Yes ,I am getting there. Another (silly) question. Can you give matrix representations of Cl(0,6) or Cl(0,8) similarily ( or for that matter any Cl(0,2n) )?
Clifford algebras are mathematical structures that extend the idea of complex numbers to higher dimensions. They are named after the mathematician William Kingdon Clifford and are used in a variety of fields, including physics, engineering, and computer science.
Matrix representations allow us to visualize and manipulate the elements of a Clifford algebra. This is particularly useful in applications where the algebra is used to study geometric transformations, such as in computer graphics or robotics.
Matrix representations become more complex as the dimension of the Clifford algebra increases. This is because the number of basis elements and the number of possible combinations also increase. In higher order Clifford algebras, matrix representations may involve higher dimensional matrices or even tensors.
Clifford algebras have been used in theoretical physics to study phenomena such as spin, electromagnetism, and quantum mechanics. They have also been used in the development of supersymmetry and string theory.
As the dimension of the Clifford algebra increases, the size and complexity of the matrices used in representations also increase. This can make calculations and manipulations more challenging. Additionally, in some cases, matrix representations may not be possible for certain types of higher order Clifford algebras.