Unified theory for external and internal attributes and symmetries of fundamental fermions (original) (raw)

Algebraic description of external and internal attributes of fundamental fermions

Journal of Physics: Conference Series, 2012

To describe external and internal attributes of fundamental fermions, a theory of multi-spinor fields is developed on an algebra, a triplet algebra, which consists of all the tripledirect-products of Dirac γ-matrices. The triplet algebra is decomposed into the product of two subalgebras, an external algebra and an internal algebra, which are exclusively related with external and internal characteristic of the multi-spinor field named triplet fields. All elements of the external algebra which is isomorphic to the original Dirac algebra Aγ are invariant under the action of permutation group S3 which works to exchange the order of the Aγ elements in the triple-direct-product. The internal algebra is decomposed into the product of two 4 2 dimensional algebras, called the family and color algebras, which describe the family and color degrees of freedom. The family and color algebras have fine substructures with ''trio plus solo'' ( 3 + 1 ) conformations which are irreducible under the action of S3. The triplet field has trio plus solo family modes with ordinary tricolor quark and colorless solo lepton components. To incorporate the Weinberg-Salam mechanism, it is required to introduce two types of triplet fields, a lefthanded doublet and right-handed singlets of electroweak iso-spin. It is possible to qualify the Yukawa interaction and to make a new interpretation of its coupling constants naturally in an intrinsic mechanism of the triplet field formalism. The ordinary Higgs mechanism leads to a new type of the Dirac mass matrices which can explain all data of quark sector within experimental accuracy.

New Algebraic Unified Theory of Leptons and Quarks

Progress of Theoretical Physics, 1987

A new algebraic theory is developed to describe the characteristic features of leptons and quarks as a whole. A pair of master fields with up and down 'weak-isospin is introduced and postulated to obey the generalized Dirac equations with coefficient matrices which belong to an algebra, a triplet algebra, consisting of triple-direct-products of Dirac's I-matrices. The triplet algebra is decomposed into three subalgebras, in a non-intersecting manner, which describe respectively the external Lorentz symmetry, the internal colour symmetry and the degrees of freedom for fourfold-family-replication of fundamental fermionic particle modes. The master fields belonging to a 64 dimensional multi-spinor space form non-irreducible representations of the Lorentz group and represent fourfold-replications of families of spin 1/2 particles, each one of which accomodates triply-degenerate quark modes and singlet leptonic modes. Canonical quantization of master fields leads naturally to the renormalizable unified field theories of fundamental fermions with universal gauge interactions of local symmetries having the route of descent from SUc(4) x SUL(2) x SUR(2) to SUc(3) x SUL(2) x Uy(l).

Spinor Structure and Internal Symmetries

International Journal of Theoretical Physics. – 2015. – Vol. 54, № 10. – P. 3533–3576. , 2015

Space-time 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 is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries P , T and their combination P T are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation C is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation C allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Quotient representations of the Lorentz group and their possible relations with P-and CP-violations are considered. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincaré group and SU(3)-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of SU(3)). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of SU(3)-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin allows one to take a new look at the problem of mass spectrum of elementary particles.

Chiral Symmetry in the Unified Fermion Theory. III

Progress of Theoretical Physics, 1971

Quantization method is presented for the fundamental Dirac field when the Lagrangian densities are invariant under non-linear chiral U (1) XU (1) transformations. The Lagrangian densities are derived from a geometrical viewpoint that the space-time possesses the torsion caused by the field itself. The equal-time anti-commutators for the field are not c-numbers but functions of the field. The chiral symmetry may break down by the quantum effects. This quantization method is applicable to more general cases.

Unified theories for quarks and leptons based on Clifford algebras

Physics Letters B, 1980

The general standpoint is presented that unified theories arise from gauging of Clifford algebras describing the internal degrees of freedom (charge, color, generation, spin) of the fundamental fermions. The general formalism is presented and the ensuing theories for color and charge (with extension to N colors), and for generations, are discussed. The possibility of further including the spin is discussed, also in connection with generations.

Constructing the Standard Model fermions

Journal of Physics: Conference Series, 2019

The Standard Model has three generations of fermions and antifermions, each with two states of isospin, and each of these has both a lepton and a quark in three possible colour states. In total there are 48 states. No known system exists for constructing these from first principles. Here, it is suggested that the number of degrees of freedom required is a consequence of the nilpotent complexified vector-quaternion Dirac algebra, which emerges from the representation of the fundamental parameters mass, time, charge and space as a Klein-4 group, and that these degrees of freedom lead to unique structural representations of each of the individual fermions.

Chiral Symmetry in the Unified Fermion Theory. II

Progress of Theoretical Physics, 1970

Chiral U(n) X U(n) transformations are investigated in the unified theory of the fundamental Dirac field q. The transformation laws are non-linear with respect to q. It is shown in the unquantized theory that the laws can be linearized by the redefinition of the field, Q= Uq, where U is a unitary matrix depending on q and q*. Discussions are given on the conditions that U is non-singular as a function of q and q* at the origin, q=q*=O. It is f'hown that the transformation from q to Q is in general neither canonical in the unquantized theory nor unitary in the quantized theory.

The Dirac Equation in Six-dimensional SO(3, 3) Symmetry Group and a Non-chiral "Electroweak" Theory

We propose a model of electroweak interactions without chirality in a sixdimensional spacetime with 3 time-like and 3 space-like coordinates, which allows a geometrical meaning for gauge symmetries. The spacetime interval ds 2 = dx μ dx μ is left invariant under the symmetry group SO(3, 3). We obtain the six-dimensional version of the Dirac gamma matrices, μ , and write down a Dirac-like Lagrangian density, L = iψ μ ∇ μ ψ. The spinor ψ can be decomposed into two Dirac spinors, ψ 1 and ψ 2 , interpreted as the electron and neutrino fields, respectively. In six-dimensional spacetime the electron and neutrino fields appear as parts of the same entity in a natural manner. The SO(3, 3) Lorentz symmetry group is locally broken to the observable SO(1, 3) Lorentz group, with only one observable time component, t z. The t z-axis may not be the same at all points of the spacetime, and the effect of breaking the SO(3, 3) spacetime symmetry group locally to an SO(1, 3) Lorentz group, is perceived by the observers as the existence of the gauge fields. We interpret the origin of mass and gauge interactions as a consequence of extra time dimensions, without the need of introducing the so-called Higgs mechanism for the generation of mass. Further, in our 'toy' model, we are able to give a geometric meaning to the electromagnetic and non-Abelian gauge symmetries.