Related papers: Quaternion Weyl Transform and some uniqueness resu…
In this paper we give an extensive description of Weyl quadratic gravity as the gauge theory of the Weyl group. The previously discovered (vectorial) torsion/non-metricity equivalence is shown to be built-in as it corresponds to a…
For a cyclic group $A$ and a connected Lie group $G$ with an $A$-module structure (with the additional conditions that $G$ is compact and the $A$-module structure on $G$ is 1-semisimple if $A\cong\ZZ$), we define the twisted Weyl group…
On four-dimensional closed manifolds we introduce a class of canonical Riemannian metrics, that we call weak harmonic Weyl metrics, defined as critical points in the conformal class of a quadratic functional involving the norm of the…
It is known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply by half-angle…
We show that Quantum Mechanics can be interpreted as a modification of the Euclidean nature of 3-d space into a particular Weyl affine space which we call Q-wis. This is proved using the Bohm-de Broglie causal formulation of Quantum…
We continue the study of the question of when a pseudo-Riemannain manifold can be locally characterised by its scalar polynomial curvature invariants (constructed from the Riemann tensor and its covariant derivatives). We make further use…
In this paper we propose the precise Wigner-Weyl calculus for the lattice models defined on the honeycomb lattice. We construct two symbols of operators: the $\mathscr{B}$-symbol, which is similar to the symbol introduced by F. Buot, and…
On any manifold, any non-degenerate symmetric 2-form (metric) and any skew-symmetric (differential) form W can be reduced to a canonical form at any point, but not in any neighborhood: the respective obstructions being the Riemannian tensor…
We develop the bivector formalism in higher dimensional Lorentzian spacetimes. We define the Weyl bivector operator in a manner consistent with its boost-weight decomposition. We then algebraically classify the Weyl tensor, which gives rise…
Let (g,k) be a reductive symmetric superpair of even type, i.e. so that there exists an even Cartan subspace a in p. The restriction map S(p^*)^k->S(a^*)^W where W=W(g_0:a) is the Weyl group, is injective. We determine its image explicitly.…
The most recent generalization of octonion Fourier transform (OFT) is the octonion linear canonical transform (OLCT) that has become popular in present era due to its applications in color image and signal processing. On the other hand the…
In this paper, we study closed four-dimensional manifolds. In particular, we show that under various new pinching curvature conditions (for example, the sectional curvature is no more than 5/6 of the smallest Ricci eigenvalue) then the…
In previous work we have shown that the (\theta->\infty)-limit of \phi^4_4-quantum field theory on noncommutative Moyal space is an exactly solvable matrix model. In this paper we translate these results to position space. We show that the…
The quadratic phase Fourier transform QPFT is a neoteric addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier…
Nonsymmorphic symmetries can enforce band connectivity that obstructs a single-band Wannier description. We show that a fractional translation $\mathcal{L}$ connecting distinct high-symmetry Wyckoff positions generically renders the Wannier…
For an arbitrary simple Lie algebra $\g$ and an arbitrary root of unity $q,$ the closed subsets of the Weyl alcove of the quantum group $U_q(\g)$ are classified. Here a closed subset is a set such that if any two weights in the Weyl alcove…
The main goal is to interpret the Askey-Wilson function and the corresponding transform pair on the quantum SU(1,1) group. A weight on the C^*-algebra of continuous functions vanishing at infinity on the quantum SU(1,1) group is studied,…
In this work, we present straightforward and concrete computations of the unitary irreducible representations of the Euclidean motion group $M(2)$ employing the methods of deformation quantization. Deformation quantization is a quantization…
We discuss the deformed function algebra of a simply connected reductive Lie group G over the complex numbers using a basis consisting of matrix elements of finite dimensional representations. This leads to a preferred deformation, meaning…
The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n).Sp(1), QKT-connection. We study the geometry of…