相关论文: The intermediate fermionic species created by $SO(…
The covering of the affine symmetry group, a semidirect product of translations and special linear transformations, in $D \geq 3$ dimensional spacetime is considered. Infinite dimensional spinorial representations on states and fields are…
The Dirac equation is solved for two novel terms which describe the interaction energy between the half integral spin of a fermion and the classical, circularly polarized, electromagnetic field. A simple experiment is suggested to test the…
The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection…
Interaction-driven topological phase transitions in Dirac semimetals are investigated by means of large-scale quantum Monte Carlo (QMC) simulations. The interaction among Dirac fermions is introduced by coupling them to Ising spins that…
It is usually supposed that the Dirac and radiation equations predict that the phase of a fermion will rotate through half the angle through which the fermion is rotated, which means, via the measured dynamical and geometrical phase…
The scattering of Dirac fermions in the background fields of topological solitons of the $(2+1)$-dimensional nonlinear $O(3)$ $\sigma$-model is studied using both analytical and numerical methods. General formulae describing fermion…
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…
Low energy weak interactions calculations with fermions frequently involve a superposition of quartic products of Dirac spinors, in which the order of the spinors is not the same in all the contributing terms. A common trick that is used to…
The fermion mass matrix, in addition to having eigenvalues (masses) which run, also changes its orientation (rotates) with changing energy scales. This means that its eigenstates at one scale will no longer be eigenstates at another scale,…
The structure of the mass matrix, a challenging problem in the Standard Model, is closely related to flavor phenomenology and the understanding of the Yukawa interaction. We derive a factorized mass structure based on observed fermion mass…
We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of…
Requiring physical consistency in a classical flat spacetime geometrisation of fermions is shown to suggest the introduction of torsion. A resulting simple model for that torsion produces a localised quantum-like particle as a solution of a…
We report discovery of a topological Mott insulator in strongly-correlated Dirac semimetals. Such an interaction-driven topological state has been theoretically proposed but not yet observed with unbiased large scale numerical simulations.…
A realization of Majorana fermions is proposed in the frustrated magnets via the topological proximity effect. Specifically, we consider a theoretical model, where a topological insulator is coupled to a frustrated magnetic material through…
{We present the results of a numerical investigation of SU(2) gauge theory with $N_f=3/2$ flavours of fermions, corresponding to 3 Majorana fermions, which transform in the adjoint representation of the gauge group. At two values of the…
The framed standard model (FSM) suggested earlier, which incorporates the Higgs field and 3 fermion generations as part of the framed gauge theory structure, is here developed further to show that it gives both quarks and leptons…
We present an analysis of the Dirac equation when the spin symmetry is changed from SU(2) to the quaternion group, $Q_8$, achieved by multiplying one of the gamma matrices by the imaginary number, $i$. The reason for doing this is to…
The Dirac equation, in the field of a traveling circularly polarized electromagnetic wave and a constant magnetic field, has singular solutions, corresponding the expansion of energy in vicinity of some singular point. These solutions…
Dirac matrices, also known as gamma matrices, are defined only up to a similarity transformation. Usually, some explicit representation of these matrices is assumed in order to deal with them. In this article, we show how it is possible to…
Fermionic continuous spin field propagating in (A)dS space-time is studied. Gauge invariant Lagrangian formulation for such fermionic field is developed. Lagrangian of the fermionic continuous spin field is constructed in terms of triple…