The definition of quasi-local mass for a bounded space-like region Ω in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary two-surface Σ = ∂Ω and should be independent of whichever space-like region Σ bounds. An important idea which is related to the Hamiltonian formulation of general ...

The Future Tube T + n of n-dimensional Minkowski spacetime may be identified with the reduced phase space P , or " space of motions " of a particle moving in (n + 1)-dimensional Anti-de-Sitter Spacetime. Both are isomorphic to a homogeneous bounded domain in C n whose Shilov boundary may be identified with n-dimensional conformally compactified Minkowski spacetime.

In this letter we work out the deformations of some flag manifolds and of complex Minkowski space viewed as an affine big cell inside G(2, 4). All the deformations come in tandem with a coaction of the appropriate quantum group. In the case of the Minkowski space this allows us to define the quantum conformal group. We also give two involutions on the quantum complex Minkowski space, that respe...

A new deformation of the of the Poincaré group and of the Minkowski space-time is given. From the mathematical point of view this deformation is rather quantum-braided group. Global and local structure of this quantumbraided Poincaré group is investigated. A kind of “quantum metrics” is introduced in the q-Minkowski space.

We discuss some aspects of the differential geometry of curves in Minkowski space. We establish the Serret-Frenet equations in Minkowski space and use them to give a very simple proof of the fundamental theorem of curves in Minkowski space. We also state and prove two other theorems which represent Minkowskian versions of a very known theorem of the differential geometry of curves in tridimensi...