Related papers: Flipped Quartification and a composite $b$-quark
The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…
We exhibit several families of Fano threefolds with a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological subring of the Chow ring of powers of these threefolds injects into…
In tri-partite systems, there are three basic biseparability, $A$-$BC$, $B$-$CA$ and $C$-$AB$ biseparability according to bipartitions of local systems. We begin with three convex sets consisting of these basic biseparable states in the…
Group theoretic method for the systematic study of multi-quark states is developed. The calculation of matrix elements of many body Hamiltonian is simplified by transforming the physical bases (quark cluster bases) to symmetry bases (group…
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
A simple integral that illustrates the concepts of regularization, subtraction, renormalization and renormalization group employed in perturbative quantum field theory(PQFT) is considered.
Treating an integrable quad-equation along with its two generalised symmetries as a compatible system allows one to construct an auto-B\"acklund transformation for solutions of the related NLS-type system. A fixed periodic reduction of the…
We generalize the problem of coin flipping to more than two outcomes and parties. We term this problem dice rolling, and study both its weak and strong variants. We prove by construction that in quantum settings (i) weak N-sided dice…
Using a set of rephasing-invariant variables, it is shown that the renormalization group equations for quark mixing parameters can be written in a form that is compact, in addition to having simple properties under flavor permutation. We…
Several matrix variate hypergeometric type distributions are derived. The compound distributions of left-spherical matrix variate elliptical distributions and inverted hypergeometric type distributions with matrix arguments are then…
Bifractional transformations which lead to quantities that interpolate between other known quantities, are considered. They do not form a group, and groupoids are used to described their mathematical structure. Bifractional coherent states…
Over the last decades quaternions have become a crucial and very successful tool for attitude representation in robotics and aerospace. However, there is a major problem that is continuously causing trouble in practice when it comes to…
We present the detailed process of converting the classical Fourier Transform algorithm into the quantum one by using QR decomposition. This provides an example of a technique for building quantum algorithms using classical ones. The…
\noindent We propose a set of rules for constructing composite leptons and quarks as triply occupied quasiparticles, in the quaternionic quantum mechanics of a pair of Harari-Shupe preons $T$ and $V$. The composites fall into two classes,…
Introducing classical fields, we can transfer entanglement completely from discrete qubits into entangled coherent state. The entanglement also can be retrieved from the continuous-variable state of the cavities to the atomic qubits. Via…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
The resummed expression for the quark form factor illustrates the fact that dimensional continuation provides a regularization not only for ultraviolet and infrared singularities of fixed order QCD amplitudes, but also for the Landau pole…
In order to study graded Frobenius algebras from a ring theoretical perspective, we introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter ones, and we investigate the structure and representations…
A family of rank-n (n=5,6,7,8) three-qubit mixed states are constructed. The explicit expressions for the three-tangle and optimal decompositions for all these states are given. The CKW relations for these states are also discussed.
The new quarks of a fourth family are being pushed into the strongly interacting regime due to the lower limits on their masses. The theoretical basis and experimental implications of such quarks are compared with exotic quarks.