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Equivalence between algebraic structures generated by parastatisticstriple relations of Green (1953) and Greenberg -- Messiah (1965), and certain orthosymplectic $mathbb{Z}_2times mathbb{Z}_2$-graded Lie superalgebras is found explicitly. Moreover, it is shown that such superalgebras give more complex para-Fermi and para-Bose systems then ones of Green -- Greenberg -- Messiah.
We comment on the recently reiterated claim that the contribution of the W-boson loop to the Higgs boson decay into two photons leads to different expressions in the $R_xi$ gauge and the unitary gauge. By applying a gauge-symmetry preserving regulari
We continue to study doubled aspects of algebroid structures equipped with the C-bracket in double field theory (DFT). We find that a family of algebroids, the Vaisman (metric or pre-DFT), the pre- and the ante-Courant algebroids are constructed by t
The Monty Hal problem is an attractive puzzle. It combines simple statement with answers that seem surprising to most audiences. The problem was thoroughly solved over two decades ago. Yet, more recent discussions indicate that the solution is incomp
We construct various systems of coherent states (SCS) on the $O(D)$-equivariant fuzzy spheres $S^d_Lambda$ ($d=1,2$, $D=d!+!1$) constructed in [G. Fiore, F. Pisacane, J. Geom. Phys. 132 (2018), 423-451] and study their localizations in configuration
We present the geometric formulation of gravity based on the mathematical structure of a Lie Algebroid. We show that this framework provides the geometrical setting to describe the gauge propriety of gravity.