Related papers: Standard model physics from an algebra?
This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory including some recent results. It is based on the algebraic approach where the starting point is a star-algebra and on the geometric…
The properties of elementary particles and their interactions at different stages of the evolution of the Universe, starting with the Planck energy $ 10 ^{19} $ GeV, are presented. We assume that the Standard Model gauge group becomes…
For the first time it is shown that the logic of quantum mechanics can be derived from Classical Physics. An orthomodular lattice of propositions, characteristic of quantum logic, is constructed for manifolds in Einstein's theory of general…
It is demonstrated how all the mechanical equations of classical electrodynamics (CEM) may be derived from only Coulomb's inverse square force law, special relativity and Hamilton's Principle. The instantaneous nature of the Coulomb force…
In a recent publication the I showed how the geometric algebra ${G}_{4,1}$, the algebra of 5-dimensional space-time, can generate relativistic dynamics from the simple principle that only null geodesics should be allowed. The same paper…
A simple extension of the Standard Model (SM), based on the gauge group $SU(3)_C\otimes SU(3)_L\otimes U(1)_Y$ with $Y$ being the hypercharge, is considered. We show that, by imposing an approximate global $SU(2)_L\times SU(2)_R$ custodial…
We introduce a new formulation of the real-spectral-triple formalism in non-commutative geometry (NCG): we explain its mathematical advantages and its success in capturing the structure of the standard model of particle physics. The idea,…
The operator manifold formalism (part I) enables the unification of the geometry and the field theory, and yields the quantization of geometry. This is the mathematical framework for our physical outlook that the geometry and fields, with…
A new approach to classical electrodynamics is presented, showing that it can be regarded as a particular case of the most general relativistic force field. In particular, at first it is shown that the structure of the Lorentz force comes…
We develop a machine learning method for mapping data originating from both Standard Model processes and various theories beyond the Standard Model into a unified representation (latent) space while conserving information about the…
The Standard Model of elementary particle physics is one of the most successful models of contemporary theoretical physics being in full agreement with experiments. However, its mathematical structure deserves further investigations both…
These lectures provide an introduction to the basic aspects of the Standard Model, $SU(3)_{C} \times SU(2)_{L} \times U(1)_{Y}$.
We consider a gauge model based on $SU(3)\otimes U(1)$ symmetry in which the lepton number is violated explicitly by charged scalar and gauge bosons, including a vector field with double electric charge. Although there exist in the…
We argue that the definition of the thermodynamic work done on a charged particle by a time-dependent electromagnetic field is an open problem, because the particle's Hamiltonian is not gauge-invariant. The solution of this problem demands…
We develop an unified algebraic approach to the description of gauge interactions within the framework of a new concept of quantum mechanics. The next step in generalizing the space-time and the action vector space is made. The gauge field…
The Standard Model is an up-to-date theory that best summarizes current knowledge in particle physics. Although some problems still remain open, it represents the leading model which all physicists refer to. One of the pillars which…
The Standard Model has three generations of fermions and although it does not contain any explicit reason for this, the existence of additional generations is now very constrained by experiment. Present measurements are saturating…
The problem of a calculation of parameters of the Standard Model is considered in the framework of the compensation approach. Conditions for a spontaneous generation of effective interactions of fundamental fields are shown to lead to sets…
The paper surveys recent progress in the search for an appropriate internal space algebra for the Standard Model (SM) of particle physics. As a starting point serve Clifford algebras involving operators of left multiplication by octonions.…
We examine the Standard Model under the electroweak symmetry group $U_{EW}(2)$ subject to the Lie algebra condition $\mathfrak{u}_{EW}(2)\not\cong \mathfrak{su}_{I}(2)\oplus \mathfrak{u}_{Y}(1)$. Physically, the condition ensures that all…