Related papers: Inequivalent quantizations from gradings and ${\ma…
We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. We begin by examining two different classes of interacting theories of massless spin 2 particles -- gravitons. One…
On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the…
A $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded generalisation of the quantum superplane is proposed and studied. We construct a bicovariant calculus on what we shall refer to as the \emph{double-graded quantum superplane}. The commutation…
We classify the admissible types of constraint (hermitian, holomorphic, with reality conditions on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors. We further point out which constrained…
We discuss the feasibility of seeing a Higgs boson which decays to four partons through a pair of (pseudo-)scalars at the LHC. We restrict our search to Higgs bosons produced in association with a W/Z boson at high transverse momentum. We…
We determine the mean number of 2-torsion elements in class groups of cubic orders, when such orders are enumerated by discriminant. Specifically, we prove that when isomorphism classes of totally real (resp., complex) cubic orders are…
Due to selection rules, new particles are sometimes discovered/predicted to be produced in pairs. In the current search for SUSY particles this will occur if R-parity is conserved. In local relativistic field theory, there can be identical…
The role of gauge invariance is reconsidered by "deriving it without assuming it" within an autonomous approach to interactions of Standard Model particles. In this approach, the renormalizable interactions are purely constrained by quantum…
Quantum correlations of identical particles are important for quantum-enhanced technologies. The recently introduced non-standard approach to treat identical particles [G. Compagno et al., Phil. Trans. R. Soc. A 376, 20170317 (2018)] is…
In the presence of symmetries, one-dimensional quantum systems can exhibit topological order, which in many cases can be characterized by a quantized value of the many-body geometric Zak or Berry phase. We establish that this topological…
We study polynomial identities of nonassociative algebras constructed by using infinite binary words and their combinatorial properties. Infinite periodic and Sturmian words were first applied for constructing examples of algebras with…
Reduction of a state of a quantum system to a subsystem gives partial quantum information about the true state of the total system. Two subalgebras A1 and A2 of B(H) are called complementary if the traceless subspaces of A1 and A2 are…
We classify multipartite entanglement in a unified manner, focusing on a duality between the set of separable states and that of entangled states. Hyperdeterminants, derived from the duality, are natural generalizations of entanglement…
We study bipartite entanglement in systems of N identical bosons distributed in M different modes. For such systems, a definition of separability not related to any a priori Hilbert space tensor product structure is needed and can be given…
Manifest gauge-invariance requires that observable states in the standard-model are described by composite operators, which involve additional Higgs contributions beyond perturbation theory. This field-theoretical effect has been confirmed…
Definitions of the parastatistics algebras and known results on their Lie (super)algebraic structure are reviewed. The notion of super-Hopf algebra is discussed. The bosonisation technique for switching a Hopf algebra in a braided category…
Determining the spin of any new particle is critical in identifying the true theory among various extensions of the Standard Model (SM). The degree of $Z$-boson polarization in any two-body decay process $A\to B Z$ is sensitive to the spin…
The algebra of differential invariants under $SA_3(\mathbb{R})$ of generic parabolic surfaces $S^2 \subset \mathbb{R}^3$ with nonvanishing Pocchiola $4^{\text{th}}$ invariant $W$ is shown to be generated, through invariant differentiations,…
The teleparallel equivalent of higher order Lagrangians like $L_{\Box R}=-R+a_{0}R^{2}+a_{1}R\Box R$ can be obtained by means of the boundary term $B=2\nabla_{\mu}T^{\mu}$. In this perspective, we derive the field equations in presence of…
We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different…