相关论文: Spherical Continuous Wavelet Transforms arising fr…

We study locally conformally homogeneous Lorentzian manifolds of dimension at least $3$, admitting an essential pseudo-group of local conformal transformations. Generalizing a recent result of Alekseevsky and Galaev, we show that any such…

All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations…

We consider quantum graphs with spin-orbit couplings at the vertices. Time-reversal invariance implies that the bond S-matrix is in the orthogonal or symplectic symmetry class, depending on spin quantum number s being integer or…

Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups.…

It was shown that in the small Wigner group there is a one-parameter subgroup of the Lorentz transformations, which leave unchanged not only the momentum of the fermion with spin h/2, but also its spin characteristics. This is the group of…

The analysis of the relation between modular P$_1$CT-symmetry -- a consequence of the Unruh effect -- and Pauli's spin-statistics relation is continued. The result in the predecessor to this article is extended to the Lorentz symmetric…

We study the quantum deformation of the Barrett-Crane Lorentzian spin foam model which is conjectured to be the discretization of Lorentzian Plebanski model with positive cosmological constant and includes therefore as a particular sector…

Starting with an integrable unitary representation of a locally compact group and its associated voice transform, coorbit theory describes the construction and investigation of the so-called coorbit spaces. A coorbit space consists of…

A group structure of the discrete transformations (parity, time reversal and charge conjugation) for spinor field in de Sitter space are studied in terms of extraspecial finite groups. Two $CPT$ groups are introduced, the first group from…

Let $X$ be a prehomogeneous vector space under a connected reductive group $G$ over $\mathbb{R}$. Assume that the open $G$-orbit $X^+$ admits a finite covering by a symmetric space. We study certain zeta integrals involving (i) Schwartz…

We prove that if a 1-connected non-conformally flat conformal Lorentzian manifold $(M,c)$ admits a connected essential transitive group of conformal transformations, then there exists a metric $g\in c$ such that $(M,g)$ is a complete…

It is commonly claimed in the recent literature that certain solutions to wave equations of positive energy of Dirac-type with internal variables are characterized by a non-thermal spectrum. As part of that statement, it was said that the…

We study the bipartite entanglement of two general classes of heterogeneous spin-($1,\frac 12$) and homogeneous spin-1 systems. By employing the spin correlation functions, we obtain the reduced two-spin density matrix (DM) and the…

While conformal transformations of the plane preserve Laplace's equation, Lorentz-conformal mappings preserve the wave equation. We discover how simple geometric objects, such as quadrilaterals and pairs of crossing curves, are transformed…

We consider a field theory with target space being the two dimensional sphere S^2 and defined on the space-time S^3 x R. The Lagrangean is the square of the pull-back of the area form on S^2. It is invariant under the conformal group…

Einstein's photo-electric effect allows us to regard electromagnetic waves as massless particles. Then, how is the photon helicity translated into the electric and magnetic fields perpendicular to the direction of propagation? This is an…

We investigate the Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it exists. In this sector quantum…

We study solutions to the Dirac equation in Minkowski space $\mathbb{R}^{1,d+1}$ that transform as $d$-dimensional conformal primary spinors under the Lorentz group $SO(1,d+1)$. Such solutions are parameterized by a point in $\mathbb{R}^d$…

We present an alternative formulation of quantum mechanical angular momentum, based on spatial wavefunctions that depend on the Euler angles $\phi, \theta, \chi$, and have an additional internal projection $n$. The wavefunctions are Wigner…

A general approach to compute the spherical measure of submanifolds in homogeneous groups is provided. We focus our attention on the homogeneous tangent space, that is a suitable weighted algebraic expansion of the submanifold. This space…