Lattice space-time from Poincaré and κ-Poincaré algebras

Modified Relativity from the κ - deformed Poincaré Algebra

The theory of the κ-deformed Poincaré algebra is applied to the analysis of various phenomena in special relativity, quantum mechanics and field theory. The method relies on the development of series expansions in κ −1 of the generalised Lorentz transformations, about the special-relativistic limit. Emphasis is placed on the underlying assumptions needed in each part of the discussion, and on i...

Poincaré Duality Algebras Mod Two

Poincaré Duality and Commutative Differential Graded Algebras

We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincaré duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincaré du-ality in the same dimension. This has application in particular to the study of CDGA models of configuration spaces on a closed manifold.

Poincaré recurrence theorem in MV-algebras

The classical Poincaré weak recurrence theorem states that for any probability space (Ω,S, P ), any P -measure preserving transformation T , and any A ∈ S, almost all points of A return to A. In the present paper the Poincaré theorem is proved when the σ-algebra S is replaced by any σ-complete MV-algebra. Keywords— Measure preserving transformation, Poincaré recurrence theorem, σ-complete MV-al...

Symmetries Shared by the Poincaré Group and the Poincaré Sphere

Henri Poincaré formulated the mathematics of Lorentz transformations, known as the Poincaré group. He also formulated the Poincaré sphere for polarization optics. It is shown that these two mathematical instruments can be derived from the two-by-two representations of the Lorentz group. Wigner’s little groups for internal space-time symmetries are studied in detail. While the particle mass is a...