Related papers: Spacetime Grand Unified Theory
Spin of elementary particles is the only kinematic degree of freedom not having classical corre- spondence. It arises when seeking for the finite-dimensional representations of the Lorentz group, which is the only symmetry group of…
This is the second part of an article about q-deformed analogs of spinor calculus. The considerations refer to quantum spaces of physical interest, i.e. q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski…
We conjecture how the particle content of the standard model can emerge starting with a supersymmetric Wess-Zumino model in 1+1 dimensions (d = 2) with three real boson and fermion fields. Considering SU(3) transformations, the lagrangian…
A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted…
We declare that we are living in the quantum 4-dimensional Minkowski space-time with the force-fields gauge-group structure $SU_c(3) \times SU_L(2) \times U(1) \times SU_f(3)$ built-in from the very beginning. From this overall background,…
The new spinor-unit field representation of the electromagnetism \cite{Nash2010} (with quark and lepton sources) is integrated via minimal coupling with standard Einstein gravitation, to formulate a Lagrangian model of the very early…
According to Two-Time Physics, there is more to space-time than can be garnered with the ordinary formulation of physics. Two-Time Physics has shown that the Standard Model of Particles and Forces is successfully reproduced by a two-time…
The quantized canonical space-time coordinates of a relativistic point particle are expressed in terms of the elements of a complex Clifford algebra which combines the complex properties of SL(2.C) and quantum mechanics. When the quantum…
We present a new unification of the electro-weak and gravitational interactions based on the joining the weak SU(2) gauge fields with the left handed part of the space-time connection, into a single gauge field valued in the…
U(4) local transformations on the four Weyl spinors forming the isospin doublet of Dirac fermions are assumed as symmetries of the standard model. With the Lorentz transformations considered simultaneously, the symmetry group is enlarged in…
In this work we produce a classical Lagrangian description of an elementary spinning particle which satisfies Dirac equation when quantized. We call this particle a classical Dirac particle. We analyze in detail the way we arrive to this…
We establish an equivalence between massive spinning particle models in four spacetime dimensions coupled to electromagnetism or gravity, within the spin-magnitude-preserving sector. Four representative models in the literature are shown to…
We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using…
The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is described in detail. CCGG emerges naturally in the Palatini formulation, where the vierbein and the spin connection are independent fields. Neither torsion nor…
Spacetime is modelled by binary relations - by the classes of the automorphisms $\GL(\C^2)$ of a complex 2-dimensional vector space with respect to the definite unitary subgroup $\U(2)$. In extension of Feynman propagators for particle…
In these notes we introduce the Clifford algebra of a quadratic space using techniques from universal algebra and algebraic theory of quadratic forms. We also define the Clifford, Pin and Spin groups associated to the algebra, and study how…
Geometrical analysis of a new type of Unified Field Theoretical models follow the guidelines of previous works of the authors is presented. These new unified theoretical models are characterized by an underlying hypercomplex structure, zero…
In this paper we study a Clifford algebra generalization of the quaternions and its relationship with braid group representations related to Majorana fermions. The Fibonacci model for topological quantum computing is based on the fusion…
Redefining the vacuum state of a free two-fold $N=1$ covariant supersymmetric string action as the one with all the excited states of world-sheet fermions occupied, makes the theory anomaly free in (3+1)+4 dimensions. While in the $NS$…
We show that three generations of leptons and quarks with unbroken Standard Model gauge symmetry $SU(3)_c\times U(1)_{em}$ can be described using the algebra of complexified sedenions $\mathbb{C}\otimes\mathbb{S}$. A primitive idempotent is…