Related papers: A Set-Matrix Duality Principle for the Dirac Equat…
Anderson's theorem asserting, that symmetry of dynamic equations written in the relativisitically covariant form is determined by symmetry of its absolute objects, is applied to the free Dirac equation. Dirac matrices are the only absolute…
A simple way to accommodate dark matter is to postulate the existence of a hidden sector. That is, a set of new particles and forces interacting with the known particles predominantly via gravity. In general this leads to a large set of…
Non-zero leptonic CP phases in the neutrino sector are clear evidence for physics beyond the Standard Model and have many implications in particle physics and cosmology. Some clues to maximal Dirac CP violation $\delta_{CP}=3\pi/2$ are…
We develop relativistic wave equations in the framework of the new non-hermitian ${\cal PT}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\cal…
Chirality is a ubiquitous phenomenon in which a symmetry between left- and right-handed objects is broken, examples in nature ranging from subatomic particles and molecules to living organisms. In particle physics, the weak force is…
Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language. In particular, certain bilattices have been used to model…
Parity-time-reversal symmetry ($\mathcal{PT}$ symmetry), a symmetry for the combined operations of space inversion ($\mathcal{P}$) and time reversal ($\mathcal{T}$), is a fundamental concept of physics and characterizes the functionality of…
The Snyder model of a noncommutative geometry due to a minimal scale $\ell$, e.g. the Planck or the Compton scale, yields $\ell^2$-shift within the Einstein Hamiltonian constraint, and $\gamma^5$-term in the free Dirac equation violating CP…
This paper reports a modified axiomatic foundation of the analytic hierarchy process (AHP), where the reciprocal property of paired comparisons is broken. The novel concept of reciprocal symmetry breaking is proposed to characterize the…
Mirror fermions with masses around the weak scale could break dynamically the electroweak symmetry if they were coupled with a new strong interaction. The purpose of this talk is to show what sort of dynamics are needed in order to render…
Classical mathematics are founded within set theory, but sets don't have \emph{symmetries}. We conjecture that if we allow sets with symmetries, then many problems such as \emph{Mirror symmetry} or \emph{Homological mirror symmetry} can be…
The aim of this article is to study certain categorical-algebraic frameworks for basic homological algebra, introduced in arXiv:2404.15896, with the aim of better understanding the differences between them. We focus on homological…
The origin of fermion generations is one of the great mysteries in particle physics. We consider here a possible solution within the Standard Model framework based on a nonabelian generalization of electric-magnetic duality. First,…
We propose a new gauged $B-L$ extension of the standard model where light neutrinos are of Dirac type, naturally acquiring sub-eV mass after electroweak symmetry breaking, without any additional global symmetries. This is realised by…
We present an attempt to formulate the supersymmetric and relativistic quantum mechanics in the sense of realizing supersymmetry on the single particle level, by utilizing the equations of motion which is equivalent to the ordinary 2nd…
We develop a class of left-right symmetric theories based on the gauge group $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)$ with a generalized seesaw mechanism for generating the charged fermion masses. Neutrinos are naturally Dirac…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
This work may be defined as a modern philosophical approach to theoretical physics. Since ancient times science and philosophy evolved in parallel, thus renewing from time to time the epochal paradigms of human thought. We could not…
Recently a notion of self-duality for differential equations of maximal cuts was introduced, which states that there should be a basis in which the matrix for an {\epsilon}-factorised differential equation is persymmetric. It was observed…
An alternative interpretation of the conformal transformations of the metric is discussed according to which the latter can be viewed as a mapping among Riemannian and Weyl-integrable spaces. A novel aspect of the conformal transformation's…