Related papers: Complex space-time and the classification of eleme…
We rewrite the standard 4-dimensional Dirac equation in terms of quaternionic 2-component spinors, leading to a formalism which treats both massive and massless particles on an equal footing. The resulting unified description has the…
The problem of confinement of fermions in 1+1 dimensions is approached with a linear potential in the Dirac equation by considering a mixing of Lorentz vector and scalar couplings. Analytical bound-states solutions are obtained when the…
A free fermion without doubler is formulated on 1+D dimensional discrete Minkowski space-time. The action is not hermitian but causes no harm. In 1+3 dimensional massless case the equation describes a single species of Dirac particle in the…
It is shown that the theory of causal fermion systems gives rise to a novel mechanism for dark matter and dark energy. This mechanism is first worked out for cubical subsets of Minkowski space with periodic boundary conditions. Then it is…
We propose a new discrete symmetry in the generation space of the fundamental fermions, consistent with the observed fermion mass spectrum. In the case of the quarks, the symmetry leads to the unique prediction of a flat CKM matrix at high…
The paper proposes an alternative scenario for the emergence of baryon asymmetry in the Universe. This scenario is realized in the lattice gravity model associated with the Dirac field as follows. At ultra-high temperatures of the Grand…
Basing on the formalism of generalized Dirac equation introduced by the author already many years ago, we suggest a model of formal intrinsic interactions within leptons and quarks of three generations. In this model, the leptons and quarks…
Drawing an analogy with the Dirac theory of fermions interacting with electromagnetic and gravitational field we write down supersymmetric equations of motion and construct a superfield action for particles with spin 1/4 and 3/4…
The reduction formulas for Dirac fermions are derived, using the exact solutions of free Dirac equation on de Sitter spacetime. In the framework of the perturbation theory one studies the Green functions and derive the scatering amplitude…
It is set manifest an underlying algebraic structure of Dirac equation and solutions, in terms of Cl2 Clifford algebra projectors and ladder operators. From it, a scheme is proposed for constructing unified field theories by enlarging the…
The possibility of additional quarks and leptons beyond the three generations already established is discussed. The make-up of this Report is (I) Introduction: the motivations for believing that the present litany of elementary fermions is…
Starting with the premise that the electric charge associated with fundamental fermions (quarks and leptons) can, under certain circumstances, be appropriately represented as a real \emph{internal} 2-vector, the mathematical ``machinery''…
Recently various phenomenological implications of the existence of extra space-time dimensions have been investigated. In this letter, we construct a model with realistic fermion mass hierarchy with (large) extra dimensions beyond the usual…
The motion of a relativistic particle is linked to its spin by the Dirac equation. Remarkably, electrons in two-dimensional materials can mimic such Dirac particles but must always appear in pairs of opposite spin chirality. Using…
The K\"ahler-Dirac equation is derived on the Weitzenb\"ock space-time, which has a quadruplet of parallel vector fields as the fundamental structure. A consistent system of equations for the K\"ahler fields and parallel vector fields is…
We discuss how basic Clifford algebra and indeed all of matrix algebra and matrix representations of finite groups comes from Iterants: very elementary processes such as an alternation of plus and minus one ...+-+-+- .... One can think of…
We present a detailed classification of random Dirac hamiltonians in two spatial dimensions based on the implementation of discrete symmetries. Our classification is slightly finer than that of random matrices, and contains thirteen…
A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation…
Assuming that the leptons and quarks other than top are massless at tree level, we show that their masses may be induced by loops involving the top quark. As a result, the generic features of the fermion mass spectrum arise from…
Using 2 more time variables as the quantum hidden variables, we derive the equation of Dirac field under the principle of classical physics, then we extend our method into the quantum fields with arbitrary spin number. The spin of particle…