Related papers: Spacetime Grand Unified Theory
A theory in which 4-dimensional spacetime is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza-Klein theory. A covariant Dirac equation…
It is shown how the vector space $V_{8,8}$ arises from the Clifford algebra $Cl(1,3)$ of spacetime. The latter algebra describes fundamental objects such as strings and branes in terms of their $r$-volume degrees of freedom, $x^{\mu_1 \mu_2…
Unification ideas suggest an integral treatment of fermion and boson spin and gauge-group degrees of freedom. Hence, a generalized quantum field equation, based on Dirac's, is proposed and investigated which contains gauge and flavor…
We introduce a spacetime discretization of the Dirac equation that has the form of a quantum automaton and that is invariant upon changing the representation of the Clifford algebra, as the Dirac equation itself. Our derivation follows…
A theory in which 16-dimensional curved Clifford space (C-space) provides a realization of Kaluza-Klein theory is investigated. No extra dimensions of spacetime are needed: "extra dimensions" are in C-space. We explore the spin gauge theory…
In the old spirit of Kaluza-Klein, we consider a spacetime of the form $P = M_4 \times K$, where $K$ is the Lie group $\mathrm{SU}(3)$ equipped with a left-invariant metric that is not fully right-invariant. We observe that a complete…
The Lagrangian action for the D4-D5-E6 model of hep-th/9306011 has 8-dim spacetime V8 of the vector representation of Spin(0,8); 8-dim fermion fields S8+ = S8- of the half-spinor reps of Spin(0,8); and 28 gauge boson fields of the bivector…
A toy model for the electroweak interactions(without chirality) is proposed in a six dimensional spacetime with 3 timelike and 3 spacelike coordinates. The spacetime interval $ds^2=dx_\mu dx^\mu$ is left invariant under the symmetry group…
Building upon previous works, it is shown that two minimal left ideals of the complex Clifford algebra $\mathbb{C}\ell(6)$ and two minimal right ideals of $\mathbb{C}\ell(4)$ transform as one generation of leptons and quarks under the gauge…
The presentation makes use of geometric algebra, also known as Clifford algebra, in 5-dimensional spacetime. The choice of this space is given the character of first principle, justified solely by the consequences that can be derived from…
A geometric approach to the standard model in terms of the Clifford algebra Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into…
There are exactly three finite subgroups of SU(2) that act irreducibly in the spin 1 representation, namely the binary tetrahedral, binary octahedral and binary icosahedral groups. In previous papers I have shown how the binary tetrahedral…
Is there more to Dirac's gamma matrices than meets the eye? It turns out that gamma zero can be factorized into a product of three operators. This revelation facilitates the expansion of Dirac's space-time algebra to Clifford algebra…
By assuming that the geometry of spacetime is uniquely determined by the energy momentum tensor of matter alone, i.e. without any interactions, enables us to construct the Lagrangian from which the metric of higher dimensional spacetime…
Seven commuting elements of the Clifford algebra $Cl_{7,7}$ define seven binary eigenvalues that distinguish the $2^7=128$ states of 32 fermions, and determine their parity, electric charge and interactions. Three commuting elements of the…
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.…
'Internal spacetime' is a modification of general relativity that was recently introduced as an approximate spacetime geometric model of quantum nonlocality. In an internal spacetime, time is stationary along the worldlines of fundamental…
Based upon the unique and simple starting point of the continuous flow of time a physical theory is derived through an analysis of the elementary arithmetic composition and symmetries of this one-dimensional progression. We describe how the…
The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding…
We examine the structure of the Clifford algebra associated with a Hermitian bilinear form and apply the result to a dynamical model of the relativistic point particle. The dynamics of the particle is described by a Dirac spinor with…