Related papers: Quaternionic Spin
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…
Spinors are lightlike. How do they combine to make massive particles? We visit the zoo of Lagrangian singularities, or caustics, in spacetime projections from spin space- the phase space of lightlike, 8- spinor flows. We find that the…
It is shown (1) that Lanczos's quaternionic formulation of Dirac's equation does not lead to a solution of the problems that plague the standard spin 3/2 theory based on the Rarita-Schwinger equation, but (2) that the four-component…
We study a quantum phase transition of electrons on a two-dimensional square lattice. Our lattice model preserves the full $\mathrm{O}(4)$ symmetry of free spin-$\frac{1}{2}$ Dirac fermions on a bipartite lattice. In particular, it not only…
We investigate the possibility of a fourth sequential generation in the lepton sector. Assuming neutrinos to be Majorana particles and starting from a recent - albeit weak - evidence for a non-zero admixture of a fourth generation neutrino…
We propose a (3+1)D linear set of covariant vector equations, which unify the spin 0 ``new Dirac equation'' with its spin 1/2 counterpart, proposed by Staunton. Our equations describe a spin (0,1/2) supermultiplet with different numbers of…
The approach unifying all the internal degrees of freedom - proposed by one of us - is offering a new way of understanding families of quarks and leptons. Spinors, namely, living in d(=1+13)-dimensional space, manifest in the observed…
In the Hamiltonian picture, free spin-$1/2$ Dirac fermions on a bipartite lattice have an $O(4)$ (spin-charge) symmetry. Here we construct an interacting lattice model with an interaction $V$, which is similar to the Hubbard interaction but…
We construct coherent states of the massless and massive representations of the Poincar\'e group. They are parameterised by points on the classical state space of spinning particles. Their properties are explored, with special emphasis on…
We explore new aspects of internal fermionic shifting symmetries, present in physical systems such as free Dirac spinors and p-form tensor-spinor fields. We propose a novel procedure to gauge these global symmetries, which also introduces a…
We consider the bosonic fields which describe a particle which may exist in states with spins one and zero with different masses. All the linearly independent solutions of the equation for a free particle are obtained in the form of the…
We propose a new, chiral description for massive higher-spin particles in four spacetime dimensions, which facilitates the introduction of consistent interactions. As proof of concept, we formulate three theories, in which higher-spin…
We consider the most general axial torsion completion of gravity with electrodynamics for $\frac{1}{2}$-spin spinors in an $8$-dimensional representation of the Dirac matter field: this theory will allow to define antimatter as matter with…
In a recent paper [1], it has been proposed that relativistic wave-particle duality can be embodied in a relation that shows that the four-velocity of a particle is proportional to the Dirac four-current. In this note we bring out some…
We emphasize that the group-theoretical considerations leading to SO(10) unification of electro-weak and strong matter field components naturally extend to space-time components, providing a truly unified description of all generation…
Some new expressions are found, concerning the one-loop effective action of four dimensional massive and massless Dirac fermions in the presence of general uniform electric and magnetic fields, with $\vec E\cdot \vec H\neq 0$ and $\vec E…
Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor…
We study configurations consisting of a gravitating spinor field $\psi$ with a nonlinearity of the type $\lambda\left(\bar\psi\psi\right)^2$. To ensure spherical symmetry of the configurations, we use two spin-$\frac{1}{2}$ fields forming a…
The equations defining pure spinors are interpreted as equations of motion formulated on the lightcone of a ten-dimensional, lorentzian, momentum space. Most of the equations for fermion multiplets, usually adopted by particle physics, are…
We investigate the semiclassical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the $\alpha$ matrices to the spin-$S$ matrices and doing a certain scaling, we…