The κ-deformation of the D-dimensional Poincaré algebra (D ≥ 2) with any signature is given. Further the quadratic Poisson brackets, determined by the classical r-matrix are calculated, and the quantum Poincaré group " with noncommuting parameters " is obtained.

Every symmetric polynomial p = p(x) = p(x1, . . . , xg) (with real coefficients) in g noncommuting variables x1, . . . , xg can be written as a sum and difference of squares of noncommutative polynomials:

Quantum simulators have recently enabled experimental observations of quantum many-body systems' internal thermalization. Often, the global energy and particle number are conserved, system is prepared with a well-defined - in microcanonical subspace. However, evolution can also conserve quantities, or charges, that fail to commute each other. Noncommuting charges emerged as subfield at intersec...

Probabilities and correlations in EPR experiments. The EPR-Bohm-Aharonov [1] system of two correlated spin-half particles or qubits observed by spatially separated observers has often been used as an arena in which to probe fundamental questions about quantum theory. Typically there are four different configurations corresponding to four different experiments and one obtains no-go theorems on (...

We investigate the transformation laws of coordinates in generalizations of special relativity with two observer-independent scales. The request of covariance leads to simple formulas if one assumes noncanonical Poisson brackets, corresponding to noncommuting spacetime coordinates. ∗email: [email protected]