Related papers: Bargmann Invariants, Geometric Phases and Recursiv…
The fundamental character of a fermionic dark matter, whether it is a Dirac or Majorana particle remains a key unresolved issue whose answer would profoundly affect dark-sector phenomenology and detection strategies thereby motivates…
In this paper, we argue in favor of first-order homogeneous Lagrangians in the velocities. The relevant form of such Lagrangians is discussed and justified physically and geometrically. Such Lagrangian systems possess Reparametrization…
As an attempt to give an unified description of quark and lepton mass matrices M_f, the following mass matrix form is proposed: the form of the mass matrices are invariant under a cyclic permutation (f_1 \to f_2, f_2 \to f_3, f_3 \to f_1)…
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…
We use Majorana operators to study entanglement dynamics under random free fermion unitary evolution and projective measurements in one dimension. For certain choices of unitary evolution, namely those which swap neighboring Majorana…
We first obtain the most general and compact parametrization of the unitary transformation diagonalizing any 3 by 3 hermitian matrix H, as a function of its elements and eigenvalues. We then study a special class of fermion mass matrices,…
Neutrinoless double beta decay is a hypothetical radioactive process which, if observed, would prove the neutrino to be a Majorana fermion: a particle that is its own antiparticle. In this lecture mini-series I discuss the physics of…
We discuss the connection between observable CP violation in the lepton sector, the properties of heavy neutrinos and the baryon asymmetry of the universe in the minimal seesaw model. A measurement of the Dirac phase $\delta$ would allow to…
We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the…
Some of the outstanding questions of particle physics today concern the neutrino sector, in particular whether there are more neutrinos than those already known and whether they are Dirac or Majorana particles.There are different ways to…
For addressing the remarkable difference between neutrino and quark mixings, high-scale mixings relations (HSMR) or unification (HSMU) hypothe\ ses were proposed. These phenomenology frameworks have been explored with respect to bounds from…
The Standard Model quark and neutrino mixing matrices are of independent empirical origin, but they do suggest unification. In this paper I obtained two united one-parameter quark and neutrino mixing matrices inferred from two…
There exist both continuum and lattice regularizations of gauge theories with fermions which preserve chiral U(1) invariance ("fermion number"). Such regularizations necessarily break gauge invariance but, in a covariant gauge, one recovers…
The observed pattern of neutrino mass splittings and mixing angles indicates that their family structure is significantly different from that of the charged fermions. We investigate the implications of these data for the fermion mass…
The basic characteristics used for the description of both Dirac and Majorana massive neutrinos are studied. Currently available experimental data for these characteristics are presented with an evidence of possible anomalies beyond the…
We investigate the consequences of a generalized $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry on a scaling neutrino Majorana mass matrix. It enables us to determine definite analytical relations between the mixing angles $\theta_{12}$ and…
An essential step towards the identification of a fermion mass generation mechanism at Planck scale is to analyse massive fermions in a given quantum gravity framework. In this letter the two mass terms entering the Hamiltonian constraint…
In this paper, we explore rephasing invariant structures of the Dirac CP phase $\delta$ under an approximation $U^{e}_{13} = 0$, where the 1-3 element of the diagonalization of charged leptons $U^{e}$ is neglected. With the further…
Integrating over a continuum Majorana fermion formally yields a functional pfaffian. We show that the phase of this pfaffian is ambiguous, as it depends on the choice of basis. This ambiguity is naturally resolved within a non-perturbative…
We study the Majorana bound states arising in quasi-one-dimensional systems with Rashba spin-orbit coupling in the presence of an in-plane Zeeman magnetic field. Using two different methods, first, the numerical diagonalization of the…