Related papers: Standard Model and 4-groups
In space of d ordinary and d Grassmann coordinates, with d \ge 15, the charges unify with the spin: the Lorentz group SO(1, d-1) in Grassmann space manifests under certain conditions as SO(1,3) (in d=4 subspace) times SO(10) \supset SU(3)…
Recent work applying higher gauge theory to the superstring has indicated the presence of 'higher symmetry', and the same methods work for the super-2-brane. In the previous paper in this series, we used a geometric technique to construct a…
We consider mapping class groups \Gamma(M) = pi_0 Diff(M fix \partial M) of smooth compact simply connected oriented 4-manifolds M bounded by a collection of 3-spheres. We show that if M contains CP^2 (with either orientation) as a…
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…
These are introductory notes on symmetries in quantum field theory and how they apply to particle physics. The notes cover the fundamentals of group theory, their representations, Lie groups, and Lie algebras, along with an elaborate…
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…
We generalize a regularization method of Stumpf 1984 in the case of non-linear spinor field models to fourth order theories and to non-scalar interactions. The involved discrete symmetries can be connected with C,P,T transformations.
A novel method is developed to derive the original Dirac equation and demonstrate that it is the only Poincare invariant dynamical equation for 4-component spinor wavefunctions. New Poincare invariant generalized Dirac and Klein-Gordon…
Motivated by the simplicity and direct phenomenological applicability of field-theoretic orbifold constructions in the context of grand unification, we set out to survey the immensely rich group-theoretical possibilities open to this type…
We give a model for composite quarks and leptons based on the semisimple gauge group SU(4), with the preons in the 10 representation; this choice of gauge gluon and preon multiplets is motivated by the possibility of embedding them in an…
When four scalar fields with global Lorentz symmetry are coupled to gravity and take a vacuum expectation value breaking diffeomorphism invariance spontaneously, the graviton becomes massive. This model is supersymmetrized by considering…
Standard model is reconstructed using the generalized differential calculus extended on the discrete space $M_4\times Z_3$. $Z_3$ is necessary for the inclusion of strong interaction. Our starting point is the generalized gauge field…
In this work, we present a trinification-based grand unified theory incorporating a global $\mathrm{SU}(3)$ family symmetry that after a spontaneous breaking leads to a left-right symmetric model. Already at the classical level, this model…
We propose a universal group theoretic description of the fermion production through any type of interaction to scalar or pseudo-scalar. Our group theoretic approach relies on the group $SU(2) \times U(1)$, corresponding to the freedom in…
The group $SL(2,\mathbb{C})$ of all complex $2\times 2$ matrices with determinant one is closely related to the group $\boldsymbol{\mathcal{L}}_{+}^\uparrow$ of real $4\times 4$ matrices representing the restricted Lorentz transformations.…
We continue the program by investigating symmetric structures underlying features of the Standard Model. We then expand the symmetry to encompass translations before contraction. A field theory model emerges with the goal of replicating a…
There are many ways to embed the Lie groups of the Standard Model of Particle Physics in a Lie group of type $E_8$, but so far there is no convincing demonstration that the finite symmetries (and asymmetries) of weak hypercharge, three…
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 suggest model equations, which, from some point of view, describe local interaction of three physical fields: a field of matter, an electromagnetic field and a gravitational field. A base of the model is a field of matter described by…
A three-family non-supersymmetric model with U(3)^3 gauge symmetry is analyzed in the context of intersecting D-branes. This is equivalent to the `trinification' model extended by three U(1) factors which survive as global symmetries in the…