Related papers: Quaternion polar representation with a complex mod…
In this paper, we present an algorithm to compute a basis of the space of algebraic modular forms on the maximal order of the definite quaternion algebra of discriminant $2$, and provide a database of such bases. One of our motivations is…
To each 4x4 matrix of reals another 4x4 matrix is constructed, the so-called associate matrix. This associate matrix is shown to have rank 1 and norm 1 (considered as a 16D vector) if and only if the original matrix is a 4D rotation matrix.…
The Cayley-Dickson Construction is a generalization of the familiar construction of the complex numbers from pairs of real numbers. The complex numbers can be viewed as two-dimensional vectors equipped with a multiplication. The…
We introduce a numerical strategy to efficiently solve the out-of-equilibrium Dyson equation in the transient regime. By discretizing the equation into a compact matrix form and applying state-of-the-art matrix compression techniques, we…
We discuss an interesting duality known to occur for certain complex reflection groups, namely the duality groups. Our main construction yields a concrete, representation theoretic realisation of this duality. This allows us to naturally…
In this paper we study the compatible family of degree-4 Scholl representations $\rho_{\ell}$ associated with a space $S$ of weight $\kappa> 2$ noncongruence cusp forms satisfying Quaternion Multiplications over a biquadratic field $K$. It…
A novel integral representation for scattering phase shifts is obtained based on a modified version of Milne's phase-amplitude approach [W.E. Milne, Phys. Rev. $\mathbf{35}$, 863 (1930)]. We replace Milne's nonlinear differential equation…
We present a compact mnemonic device for computing the product of two (split) octonions written in Cayley--Dickson form q+l p with q,p in H. The rule appears as a simple (R+L) pattern of right-ordered and left-ordered (quaternionic)…
We discuss the creation of electron-positron cascades in the context of pulsar polar cap acceleration models and derive several useful analytic and semi-analytic results for the spatial extent and energy response of the cascade. Instead of…
The complete expression for the intensity in pseudo-scalar meson photoproduction with a polarized beam, target, and recoil baryon is derived using a density matrix approach that offers great economy of notation. A Cartesian basis with spins…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
Some comments are made on the matrices which serve as the basis of a quaternionic algebra. We show that these matrices are related with the quaternionic action of the imaginary units from the left and from the right.
On the received coefficients of the analytical forms for deuteron wave function in coordinate representation in form r^(l+1)*exp(-A*r) for the modern realistic nucleon-nucleon potentials NijmI, NijmII, Nijm93, Reid93 and Argonne v18 are…
The production of various heavy-quark-containing baryons in electron-positron annihilation is considered. On the basis of exact formulas that we obtained previously within full perturbation theory, new numerical calculations of the…
This is part one of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and…
New models of the Fock space sector corresponding to some fixed number of electrons are introduced. These models originate from the representability theory and their practical implementation may lead to essential reduction of dimensions of…
This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results…
We present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the algorithm is equivalent to non-factorizability for which we…
Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…
The polynomials with quaternion coefficients have two kind of roots: isolated and spherical. A spherical root generates a class of roots which contains only one complex number $z$ and its conjugate $\bar{z}$, and this class can be…