Quantum Minkowski spaces

Solutions of Klein--Gordon and Dirac equations on quantum Minkowski spaces

Covariant differential calculi and exterior algebras on quantum homogeneous spaces endowed with the action of inhomogeneous quantum groups are classified. In the case of quantum Minkowski spaces they have the same dimensions as in the classical case. Formal solutions of the corresponding Klein--Gordon and Dirac equations are found. The Fock space construction is sketched.

Multiparameter Quantum Minkowski Space-Time and Quantum Maxwell Equations Hierarchy

Earlier we have proposed new $q$ - Maxwell equations which are the first members of an infinite new hierarchy of $q$ - difference equations. We have used an indexless formulation in which all indices are traded for two conjugate variables, $z,\bar z$. Weproposed also new $q$ - Minkowski coordinates which together with $z,\bar z$ can be interpreted as the six local coordinates of a $SU_q(2,2)$ flag manifold. In the present paper we generalise the main ingredients of this construction to the multiparameter case using the seven-parameter quantum group deformation of $GL(4)$ and $U(gl(4))$ and the…

Bicovariant Calculus on Twisted ISO(N), Quantum Poincare' Group and Quantum Minkowski Space

A bicovariant calculus on the twisted inhomogeneous multiparametric $q$-groups of the $B_n,C_n,D_n$ type, and on the corresponding quantum planes, is found by means of a projection from the bicovariant calculus on $B_{n+1}$, $C_{n+1}$, $D_{n+1}$. In particular we obtain the bicovariant calculus on a dilatation-free $q$-Poincaré group $ISO_q (3,1)$, and on the corresponding quantum Minkowski space. The classical limit of the $B_n,C_n,D_n$ bicovariant calculus is discussed in detail.

Twist-related geometries on q-Minkowski space

The role of the quantum universal enveloping algebras of symmetries in constructing non-commutative geometry of the space-time including vector bundles, measure, equations of motion and their solutions is discussed. In the framework of the twist theory the Klein-Gordon-Fock and Dirac equations on the quantum Minkowski space are studied from this point of view for the simplest quantum deformation of the Lorentz algebra induced by its Cartan subalgebra twist.

Representations of q-Minkowski space algebra

The properties of the quantum Minkowski space algebra are discussed. Its irreducible representations with highest weight vectors are constructed and relations to other quantum algebras: $su_{q}(2)$, $q$-oscillator, $q$-sphere are pointed out.

非交换几何中的双交叉积与扭曲量子对称性：以 $\varrho$-Minkowski 为例

Bicrossproduct vs. twist quantum symmetries in noncommutative geometries: the case of $\varrho$-Minkowski

本文研究 $\varrho$-Minkowski 时空的量子庞加莱对称性，证明其同时具有双交叉积与 Drinfel'd 扭曲结构，并构造出关于标准积分测度循环的新非交换 $\star$-乘积。

Separation of noncommutative differential calculus on quantum Minkowski space

Noncommutative differential calculus on quantum Minkowski space is not separated with respect to the standard generators, in the sense that partial derivatives of functions of a single generator can depend on all other generators. It is shown that this problem can be overcome by a separation of variables. We study the action of the universal L-matrix, appearing in the coproduct of partial derivatives, on generators. Powers of he resulting quantum Minkowski algebra valued matrices are calculated. This leads to a nonlinear coordinate transformation which essentially separates the calculus. A com…

q-Deformed Minkowski Space based on a q-Lorentz Algebra

The Hilbert space representations of a non-commutative q-deformed Minkowski space, its momenta and its Lorentz boosts are constructed. The spectrum of the diagonalizable space elements shows a lattice-like structure with accumulation points on the light-cone.

A note on geometry of Kappa-Minkowski space

The infinitesimal action of Kappa-Poincar'e group on Kappa-Minkowski space is computed both for generators of Kappa-Poincar'e algebra and those of Woronowicz generalized Lie algebra. The notion of invariant operators is introduced and generalized Klein-Gordon equation is written out.

Quantum geodesics on $λ$-Minkowski spacetime

We apply a recent formalism of quantum geodesics to the well-known bicrossproduct model $λ$-Minkowski quantum spacetime $[x^i,t]=\imathλ_p x^i$ with its flat quantum metric as a model of quantum gravity effects, with $λ_p$ the Planck scale. As examples, quantum geodesic flow of a plane wave gets an order $λ_p$ frequency dependent correction to the classical geodesic velocity. A quantum geodesic flow with classical velocity $v$ of a Gaussian with width $\sqrt{2β}$ initially centred at the origin changes its shape but its centre of mass moves with ${<x>\over<t>}=v(1+{λ_p^2\over 2β}+O(λ^3_p))$, a…