In this study, we define Pauli–Leonardo quaternions by taking the coefficients of Pauli as Leonardo numbers. We give recurrence relation, Binet formula, generating function, exponential some special equalities, and sum properties these novel quaternions. addition, investigate interrelations between Pauli–Fibonacci, Pauli–Lucas Moreover, create algorithms that determine terms Finally, generate m...

Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce gradually necessary and sufficient conditions to be met in order to carry out the following programme: Given a group G, we first construct vector spaces over GF(p), ...

A representation of polymer self-consistent field theory equivalent to quantum density functional is given in terms non-orthogonal basis sets. Molecular integrals and equations for spherically symmetric systems using Gaussian functions are given, the binding energies radial electron densities neutral atoms hydrogen through krypton calculated. An exact self-interaction correction adopted Pauli-e...

Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce gradually necessary and sufficient conditions to be met in order to carry out the following programme: Given a group G, we first construct vector spaces over GF(p), ...

We present a general procedure for determining quasi-exact solvability of the Dirac and the Pauli equation with an underlying sl(2) symmetry. This procedure makes full use of the close connection between quasi-exactly solvable systems and supersymmetry. The Dirac-Pauli equation with spherical electric field is taken as an example to illustrate the procedure. 1. In this talk we present a general...

We introduce a technique for restoring general coordinate invariance into theories where it is explicitly broken. This is the analog for gravity of the Callan-Coleman-WessZumino formalism for gauge theories. We use this to elucidate the properties of interacting massless and massive gravitons. For a single graviton with a Planck scale MPl and a mass mg, we find that there is a sensible effectiv...