Clifford algebras, Fourier transforms, and quantum mechanics
نویسندگان
چکیده
منابع مشابه
Clifford Algebras in Symplectic Geometry and Quantum Mechanics
The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C0,2. This algebra is essentially the geometric algebra describing the rotational properties of space. Hidden within this algebra are symplectic structures with Heisenberg algebras at their core. This algebra also enab...
متن کاملQuantum Clifford Algebras
Quantum multiparameter deformation of real Clifford algebras is proposed. The corresponding irreducible representations are found.
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Clifford algebras are used for definition of spinors. Because of using spin-1/2 systems as an adequate model of quantum bit, a relation of the algebras with quantum information science has physical reasons. But there are simple mathematical properties of the algebras those also justifies such applications. First, any complex Clifford algebra with 2n generators, Cll(2n, C), has representation as...
متن کاملThe Clifford Fourier transform in real Clifford algebras
We use the recent comprehensive research [17, 19] on the manifolds of square roots of −1 in real Clifford’s geometric algebras Cl(p,q) in order to construct the Clifford Fourier transform. Basically in the kernel of the complex Fourier transform the imaginary unit j ∈ C is replaced by a square root of−1 in Cl(p,q). The Clifford Fourier transform (CFT) thus obtained generalizes previously known ...
متن کاملHistory of quaternion and Clifford Fourier transforms and wavelets
We survey the historical development of quaternion and Clifford Fourier transforms and wavelets.
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ژورنال
عنوان ژورنال: Mathematical Methods in the Applied Sciences
سال: 2012
ISSN: 0170-4214
DOI: 10.1002/mma.2679