Related papers: Flipped Quartification and a composite $b$-quark
We introduce the quasi-Hopf superalgebras which are $Z_2$ graded versions of Drinfeld's quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the…
A new kind of aperiodic tiling is introduced. It is shown to underlie a structure obtained as a superposition of waves with incommensurate periods. Its connections to other other tilings and quasicrystals are discussed.
We develop a general theory of `quantum' diffeomorphism groups based on the universal comeasuring quantum group $M(A)$ associated to an algebra $A$ and its various quotients. Explicit formulae are introduced for this construction, as well…
We investigate the relation between Connes-Kreimer Hopf algebra approach to renomalization and deformation quantization. Both approaches rely on factorization, the correspondence being established at the level of Wiener-Hopf algebras, and…
We introduce a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultradistributions we show that this complex plane-generalization overcomes all…
A quaternionic version of Quantum Mechanics is constructed using the Schwinger's formulation based on measurements and a Variational Principle. Commutation relations and evolution equations are provided, and the results are compared with…
The selfconsistent cranking approach is extended to the case of rotation about an axis which is tilted with respect to the principal axes of the deformed potential (Tilted Axis Cranking). Expressions for the energies and the intra bands…
Renormalization of composite three-quark operators in dimensional regularization is complicated by the mixing of physical and unphysical (evanescent) operators. This mixing must be taken into account in a consistent subtraction scheme. In…
In this paper, we study additively indecomposable quadratic forms over real biquadratic and simplest cubic fields. In particular, we show that over these fields, we can always find such a classical form in 2 variables, which differs from…
A modified Gibbs's rotation matrix is derived and the connection with the Euler angles, quaternions, and Cayley$-$Klein parameters is established. As particular cases, the Rodrigues and Gibbs parameterizations of the rotation are obtained.…
In this paper, we define a new transform called the Gabor quaternionic Fourier transform (GQFT), which generalizes the classical windowed Fourier transform to quaternion valued-signals, we give several important properties such as the…
The extension of the standard model with pairs of the vector-like families is studied. The quark mixing matrices for the left- and right-handed charged currents, as well as those for the flavour changing neutral currents, the Z and Higgs…
Lambek's unified classification of the elementary interaction-quanta of the ``Standard model'' is formulated in terms of the 24 units of the integer-quaternion ring, i.e., the tetrahedral group Q_{24}. An extension of Lambek's scheme to the…
The renormalization group is extended to cases where several heavy particles are decoupled at the same time. This involves large logarithms which are scale-invariant and so cannot be eliminated by a change of renormalization scheme. A set…
A cyclically ordered quiver is a quiver endowed with an additional structure of a cyclic ordering of its vertices. This structure, which naturally arises in many important applications, gives rise to new powerful mutation invariants.
We use the fusion construction in the twisted quantum affine algebras to obtain a unified method to deform the wedge product for classical Lie algebras. As a byproduct we uniformly realize all non-spin fundamental modules for quantized…
Quantum Fourier Transform (QFT) plays a principal role in the development of efficient quantum algorithms. Since the number of quantum bits that can currently built is limited, while many quantum technologies are inherently three- (or more)…
Many known models, which generally use a factorization hypothesis, give a poor account of the decays B into J/psi + K(*). Usually there is a free overall factor, which is fit to the data, so that tests of the models rely upon ratios. The…
We study twisted modules for (weak) quantum vertex algebras and we give a conceptual construction of (weak) quantum vertex algebras and their twisted modules. As an application we construct and classify irreducible twisted modules for a…
We construct a new family of N-fold supersymmetric systems which is referred to as ``type B''. A higher derivative representation of the N-fold supercharge for this new family is given by a deformation of the type A N-fold supercharge. By…