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Computational Group Theory is applied to indexed objects (tensors, spinors, and so on) with dummy indices. There are two groups to consider: one describes the intrinsic symmetries of the object and the other describes the interchange of…
All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations…
It is proved that feedback classification of a linear system over a commutative von Neumann regular ring R can be reduced to the classification of a finite family of systems, each of which is properly split into a reachable and a…
We formulate a theory of invariants for the spin symmetric group in some suitable modules which involve the polynomial and exterior algebras. We solve the corresponding graded multiplicity problem in terms of specializations of the Schur…
The recent developments of the ``connection'' and ``loop'' representations have given the possibility to show that the two representation are equivalent and that it is possible to transform any result from one representation into the other.…
We define and discuss an extension of the SpinC quantization concept to odd-dimensional manifolds. After that we describe its relation to (the usual) even-dimensional SpinC quantization and how its famous properties like "Quantization…
In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we…
The concept of quantization consists in replacing commutative quantities by noncommutative ones. In mathematical language an algebra of continuous functions on a locally compact topological space is replaced with a noncommutative…
The interrelations between the inverse problems of the representation theory and the categorical representation theory are discussed.
Entanglement represents a pure quantum effect involving two or more particles. Spin systems are good candidates for studying this effect and its relation with other collective phenomena ruled by quantum mechanics. While the presence of…
We study the influence of the spin-torsion coupling prescription and we prove the causal propagation for the fields of the standard model.
We describe quantum mechanical entanglement in terms of compact quantum groups. We prove an analog of positivity of partial transpose (PPT) criterion and formulate a Horodecki-type Theorem.
Canonical correlation analysis is a family of multivariate statistical methods for the analysis of paired sets of variables. Since its proposition, canonical correlation analysis has for instance been extended to extract relations between…
We introduce a single-set axiomatisation of cubical $\omega$-categories, including connections and inverses. We justify these axioms by establishing a series of equivalences between the category of single-set cubical $\omega$-categories,…
In this manuscript, we give a classification of all irreducible, unitary representations of complex spin groups.
We investigate the relation between Cartan decompositions of the unitary group and discrete quantum symmetries. To every Cartan decomposition there corresponds a quantum symmetry which is the identity when applied twice. As an application,…
This talk is devoted mainly to the concept of higher-order polarization on a group, which is introduced in the framework of a Group Approach to Quantization, as a powerful tool to guarantee the irreducibility of quantizations and/or…
This work is a generalization of \cite{baldiotti2021} to Grassmann algebras of arbitrary dimensions. Here we present a covariant quantization scheme for pseudoclassical theories focused on non-hermitian quantum mechanics. The quantization…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
In honor of Minkowski's great contribution to Special Relativity, celebrated at this conference, we first review Wigner's theory of the projective irreducible representations of the inhomogeneous Lorentz group. We also sketch those parts of…