相关论文: Quantum Minkowski spaces

The particle algebras generated by the creation/annihilation operators for bosons and for fermions are shown to possess quantum invariance groups. These structures and their sub(quantum)groups are investigated.

Attention is focused on antisymmetrised versions of quantum spaces that are of particular importance in physics, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. For each of…

The quantum deformed (1+1) Poincare' algebra is shown to be the kinematical symmetry of the harmonic chain, whose spacing is given by the deformation parameter. Phonons with their symmetries as well as multiphonon processes are derived from…

A general scheme of construction and analysis of physical fields on the various homogeneous spaces of the Poincar\'{e} group is presented. Different parametrizations of the field functions and harmonic analysis on the homogeneous spaces are…

We express the defining relations of the $q$-deformed Minkowski space algebra as well as that of the corresponding derivatives and differentials in the form of reflection equations. This formulation encompasses the covariance properties…

We discuss various algebraic quantum structures associated to monotone Lagrangian submanifolds and we present a number of applications, computations and examples.

Author of this article created for the first time the method for finding solutions of the Minkowski problem for closed surfaces in Riemannian space.

This thesis contains the formulation and computation of quantum isometry groups.

We determine the quantum automorphism groups of finite spaces and find they are all compact quantum groups in the sense of Woronowicz. This solves a problem of Connes for finite spaces.

We define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions -- which we call spatial partitions. This extends substantially Banica and Speicher's approach of the so…

Novel solutions of Minkowski QED2+1 and large $N_f$ QCD Schwinger-Dyson equations will be presented and discussed. The resultant propagators of confined degrees of freedom will be shown.

We propose a contraction of the de Sitter quantum group leading to the quantum Poincare group in any dimensions. The method relies on the coaction of the de Sitter quantum group on a non--commutative space, and the deformation parameter $q$…

Penrose's Spin Geometry Theorem is extended further, from $SU(2)$ and $E(3)$ (Euclidean) to $E(1,3)$ (Poincar\'e) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike…

From the modern viewpoint and by the geometric method, this paper provides a concise foundation for the quantum theory of massless spin-3/2 field in Minkowski spacetime, which includes both the one-particle's quantum mechanics and the…

Attention is focused on quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. There are algebra isomorphisms that allow to identify quantum…

A quantum frame is defined by a material object subject to the laws of quantum mechanics. The present paper studies the relations between quantum frames, which in the classical case are described by elements of the Poincare' group. The…

This is a survey of results on partially commutative groups and partially commutative algebras.

An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension D>2 is presented in these lecture notes. To start with, the one-to-one correspondence between linear relativistic…

We consider new Abelian twists of Poincare algebra describing non-symmetric generalization of the ones given in [1], which lead to the class of Lie-deformed quantum Minkowski spaces. We apply corresponding twist quantization in two ways: as…

An example of a toy model of $D=2$ Minkowski space and Poincar\'e group with real deformation parameter $q$ is considered. A notion of free motion is defined. The kinematics and phase-space are constructed and the ``uncertainity'' ralations…