Analysis on generalized Clifford algebras
نویسندگان
چکیده
Изучается вопрос, связанный с обобщенными алгебрами Клиффорда $\mathcal{C}_n(\underline{a})$, где $\underline{a}$ - ненулевой вектор. Если $\{e_1,…,e_n\}$ ортонормированный базис, операция умножения определяется соотношениями \begin{align*} e_j^2=a_je_j-1, e_ie_j+e_je_i=a_ie_j+a_je_i, \end{align*} $a_j=e_j\cdot\underline{a}$. Случай $\underline{a}=\underline{0}$ соответствует классической алгебре Клиффорда. Определяется оператор Дирака $D=\sum_je_j\partial_{x_j}$ и регулярные функции как его нулевое решение. Изучаются алгебраические свойства рассматриваемой алгебры. Доказываются основные формулы для оператора изучаются регулярных функций.
منابع مشابه
Hyperbolic Polynomials and Generalized Clifford Algebras
We consider the problem of realizing hyperbolicity cones as spectrahedra, i.e. as linear slices of cones of positive semidefinite matrices. The generalized Lax conjecture states that this is always possible. We use generalized Clifford algebras for a new approach to the problem. Our main result is that if −1 is not a sum of hermitian squares in the Clifford algebra of a hyperbolic polynomial, t...
متن کاملNotes on Weyl–Clifford algebras
Here is discussed generalization of Clifford algebras, l-dimensional Weyl–Clifford algebras T(n, l) with n generators tk satisfying equation ∑n k=1 aktk )l = ∑n k=1 (ak) . It is originated from two basic and well known constructions: representation of Clifford algebras via tensor products of Pauli matrices together with extension for l > 2 using Weyl commutation relations. Presentation of such ...
متن کاملBasic Calculations on Clifford Algebras
Clifford algebras are important structures in Geometric Algebra and Quantum Mechanics. They have allowed a formalization of the primitive operators in Quantum Theory. The algebras are built over vector spaces with dimension a power of 2 with addition and multiplication being effectively computable relative to the computability of their own spaces. Here we emphasize the algorithmic notions of th...
متن کاملGeneralized Clifford Algebras and the Last Fermat Theorem
Abstract One shows that the Last Fermat Theorem is equivalent to the statement that all rational solutions x + y = 1 of equation (k ≥ 2) are provided by an orbit of rationally parametrized subgroup of a group preserving k–ubic form. This very group naturally arrises in the generalized Clifford algebras setting [1]. I. The stroboscopic motion of the independent oscilatory degree of freedom is gi...
متن کاملClifford Algebras and Graphs
I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss other related sets of graphs. This construction can be used to build models of representations of simplylaced compact Lie groups. 1 Clifford Algebras Let A be a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ??????? ?????????? ???????????????? ???????????? ????????????
سال: 2023
ISSN: ['1814-3520', '2500-1590']
DOI: https://doi.org/10.14498/vsgtu1973