Related papers: Quantum Minkowski spaces
The cluster multiplication formulas for a generalized quantum cluster algebra of Kronecker type are explicitly given. Furthermore, a positive bar-invariant $\mathbb{Z}[q^{\pm\frac{1}{2}}]$-basis of this algebra is constructed.
This paper presents the axioms for a quantum Yang-Mills theory in the Minkowski spacetime. There are two routes of analytic continuation for the Schwinger functions, namely the Wightman functions and time-ordered products of field…
The space of time-like geodesics on Minkowski spacetime is constructed as a coset space of the Poincar\'e group in (3+1) dimensions with respect to the stabilizer of a worldline. When this homogeneous space is endowed with a Poisson…
The modified Seiberg-Witten monopole equations are presented in this letter. These equations have analytic solutions in the whole 1+3 Minkowski space with finite energy. The physical meaning of the equations and solutions are discussed…
The notions of higher-order weighted multilinear Poincar\'e and Sobolev inequalities in Carnot groups are introduced. As an application, weighted Leibnitz-type rules in Campanato-Morrey spaces are established.
The purpose of the present note is to propose, in the framework of relativistic quantum mechanics, a new Poincare-invariant equation for two particles with masses m_1, m_2 and spin s_1=s_2=1/2. It is a first-order linear differential…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
The first results, both positive and negative, recently obtained in the area of constructing stationary spinning solitons in flat Minkowski space in 3+1 dimensions are discussed.
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
Quantum substitutions of Pisot type (and their quantum topological entropy) are introduced. Their utility as algorithms for optimal spacing is analyzed.
This paper gives a brief overview of some new work in number theory and algebra, and also studies the arithmetic and algebraic properties of Minkowski balls and spheres. The content of the paper is presented in more detail in the table of…
In several of the class A Bianchi models, minisuperspaces admit symmetries. It is pointed out that they can be used effectively to complete the Dirac quantization program. The resulting quantum theory provides a useful platform to…
We present a construction of string--localized covariant free quantum fields for a large class of irreducible (ray) representations of the Poincare group. Among these are the representations of mass zero and infinite spin, which are known…
Minkowski space, conformal group, compactification, conformal infinity, conformal inversion, light cone at infinity, SU(2,2), SO(4,2), Hodge star operator, Clifford algebra, spinors, twistors, antilinear operators, exterior algebra,…
Lead by examples we introduce the notions of Hopf algebra and quantum group. We study their geometry and in particular their Lie algebra (of left invariant vectorfields). The examples of the quantum sl(2) Lie algebra and of the quantum…
In this paper, we give some characterizations for spacelike helices in Minkowski space-time. We find the differential equations characterizing the spacelike helices and also give the integral characterizations for these curves in Minkowski…
We give a survey of techniques from quantum group theory which can be used to show that some quantum spaces (objects of the category dual to the category of $\mathrm{C}^*$-algebras) do not admit any quantum group structure. We also provide…
A new space namely the Weyl-Kahler is proposed to the quantum state space. Some of the physical consequences are discussed.
We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation…
Mellin-Barnes (MB) techniques applied to integrals emerging in particle physics perturbative calculations are summarized. New versions of AMBRE packages which construct planar and nonplanar MB representations are shortly discussed. The…