Related papers: Clifford Coherent State Transforms on Spheres
We study various kinds of Grassmannians or Lagrangian Grassmannians over $\mathbb{R}$, $\mathbb{C}$ or $\mathbb{H}$, all of which can be expressed as $\mathbb{G}/\mathbb{P}$ where $\mathbb{G}$ is a classical group and $\mathbb{P}$ is a…
In this article we construct a cochain complex of a complex Clifford algebra with coefficients in itself in a combinatorial fashion and we call the corresponding cohomology by {\it Clifford cohomology.} We show that {\it Clifford…
While the Clifford (geometric) algebra Fourier Transform (CFT) is global, we introduce here the local Clifford (geometric) algebra (GA) wavelet concept. We show how for $n=2,3 (\mod 4)$ continuous $Cl_n$-valued admissible wavelets can be…
In this paper we show how to describe the general theory of a linear metric compatible connection with the theory of Clifford valued differential forms. This is done by realizing that for each spacetime point the algebra of Clifford…
We extend Kostant's results about $\mathfrak{g}$-invariants in the Clifford algebra $Cl(\mathfrak{g})$ of a complex semisimple Lie algebra $\mathfrak{g}$ to the relative case of $\mathfrak{k}$-invariants in the Clifford algebra…
We discuss how transformations in a three dimensional euclidean space can be described in terms of the Clifford algebra $\mathcal{C}\ell_{3,3}$ of the quadratic space $\mathbb{R}^{3,3}$. We show that this algebra describes in a unified way…
We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of…
For the continuous Wigner function and for certain discrete Wigner functions, permuting the values of the Wigner function in accordance with a symplectic linear transformation is equivalent to performing a certain unitary transformation on…
Several versions of the Fourier transform have been formulated in the framework of Clifford algebra. We present a (Clifford-Fourier) transform, constructed using the geometric properties of Clifford algebra. We show the corresponding…
Clifford-Legendre and Clifford-Gegenbauer polynomials are eigenfunctions of certain differential operators acting on functions defined on $m$-dimensional euclidean space ${\mathbb R}^m$ and taking values in the associated Clifford algebra…
We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated…
$P$-, $T$-, $C$-transformations of the Dirac field in the de Sitter space are studied in the framework of an automorphism set of Clifford algebras. Finite group structure of the discrete transformations is elucidated. It is shown that $CPT$…
The monograph offers a coherent and self-contained treatment of massless (ladder) representations of the conformal group U(2,2) and their restriction to the de Sitter group Sp(2,2), combining rigorous representation-theoretic analysis with…
This paper explores the representation of quantum computing in terms of unitary reflections (unitary transformations that leave invariant a hyperplane of a vector space). The symmetries of qubit systems are found to be supported by…
We show that Clifford algebras are closely related to the study of isoclinic subspaces of spinor spaces and, consequently, to the Hurwitz-Radon matrix problem. Isocliny angles are introduced to parametrize gamma matrices, i.e., matrix…
Euclidean conformal integrals for an arbitrary number of points in any dimension are evaluated. Conformal transformations in the Euclidean space can be formulated as the Moebius group in terms of Clifford algebras. This is used to interpret…
For the complex Clifford algebra Cl(p,q) of dimension n=p+q we define a Hermitian scalar product. This scalar product depends on the signature (p,q) of Clifford algebra. So, we arrive at unitary spaces on Clifford algebras. With the aid of…
The conformal-bienergy functional $E_2^c$ is a modified version of the classical bienergy functional $E_2$ and it is conformally invariant in the case of a four-dimensional domain. The critical points of $E_2^c$ are called…
Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3+1-dimensional loop quantum gravity. The construction of…
A classical result of Gelfand shows that the topologized spectrum of characters on commutative Banach algebra is homeomorphic to the underlying space. This fact is used in solving the Calder\'on problem in dimension 2 via the boundary…