Does dark matter consist of baryons of new stable family quarks?

We investigate the possibility that the dark matter consists of clusters of the heavy family quarks and leptons with zero Yukawa couplings to the lower families. Such a family is predicted by the {\it approach unifying spin and charges} as the fifth family. We make a rough estimation of properties of baryons of this new family members, of their behaviour during the evolution of the universe and when scattering on the ordinary matter and study possible limitations on the family properties due to the cosmological and direct experimental evidences.Comment: 28 pages, revtex, submitted to Phys. Rev. Let

Dirac-K\"ahler approach connected to quantum mechanics in Grassmann space

We compare the way one of us got spinors out of fields, which are a priori antisymmetric tensor fields, to the Dirac-K\"ahler rewriting. Since using our Grassmann formulation is simple it may be useful in describing the Dirac-K\"ahler formulation of spinors and in generalizing it to vector internal degrees of freedom and to charges. The ``cheat'' concerning the Lorentz transformations for spinors is the same in both cases and is put clearly forward in the Grassmann formulation. Also the generalizations are clearly pointed out. The discrete symmetries are discussed, in particular the appearance of two kinds of the time-reversal operators as well as the unavoidability of four families.Comment: 36 page

On the origin of families of quarks and leptons - predictions for four families

The approach unifying all the internal degrees of freedom--proposed by one of us--is offering a new way of understanding families of quarks and leptons: A part of the starting Lagrange density in d(=1+13), which includes two kinds of spin connection fields--the gauge fields of two types of Clifford algebra objects--transforms the right handed quarks and leptons into the left handed ones manifesting in d=1+3 the Yukawa couplings of the Standard model. We study the influence of the way of breaking symmetries on the Yukawa couplings and estimate properties of the fourth family--the quark masses and the mixing matrix, investigating the possibility that the fourth family of quarks and leptons appears at low enough energies to be observable with the new generation of accelerators.Comment: 31 pages,revte

Quantum gates and quantum algorithms with Clifford algebra technique

We use our Clifford algebra technique, that is nilpotents and projectors which are binomials of the Clifford algebra objects $\gamma^a$ with the property $\{\gamma^a,\gamma^b\}_+ = 2 \eta^{ab}$, for representing quantum gates and quantum algorithms needed in quantum computers in an elegant way. We identify $n$-qubits with spinor representations of the group SO(1,3) for a system of $n$ spinors. Representations are expressed in terms of products of projectors and nilpotents. An algorithm for extracting a particular information out of a general superposition of $2^n$ qubit states is presented. It reproduces for a particular choice of the initial state the Grover's algorithm.Comment: 9 pages, revte

"An effective two dimensionality" cases bring a new hope to the Kaluza-Klein[like] theories

One step towards realistic Kaluza-Klein[like] theories and a loop hole through the Witten's "no-go theorem" is presented for cases which we call an effective two dimensionality cases: In $d=2$ the equations of motion following from the action with the linear curvature leave spin connections and zweibeins undetermined. We present the case of a spinor in $d=(1+5)$ compactified on a formally infinite disc with the zweibein which makes a disc curved on an almost $S^2$ and with the spin connection field which allows on such a sphere only one massless normalizable spinor state of a particular charge, which couples the spinor chirally to the corresponding Kaluza-Klein gauge field. We assume no external gauge fields. The masslessness of a spinor is achieved by the choice of a spin connection field (which breaks parity), the zweibein and the normalizability condition for spinor states, which guarantee a discrete spectrum forming the complete basis. We discuss the meaning of the hole, which manifests the noncompactness of the space.Comment: 26 pages, 1 figure, an addition which helps to clarify the assumptions and their consequences (the discreteness of spectrum, the massless solution of one handedness,..

Can the "basis vectors'', describing the internal space of point fermion and boson fields with the Clifford odd (for fermions) and Clifford even (for bosons) objects, be meaningfully extended to strings?

The {\it string theory} seems to be a mathematically consistent way for explaining so far observed fermion and boson second quantized fields, with gravity included, by offering the renormalizability of the theory by extending the point fermions and bosons into strings and by offering the supersymmetry among fermions and bosons. In a long series of works one of the authors in collaboration with another author and other collaborators, has found the phenomenological success with the model named the {\it spin-charge-family} theory with the properties: The creation and annihilation operators for fermions and bosons fields are described as tensor products of the Clifford odd (for fermions) and the Clifford even (for bosons) ``basis vectors'' and basis in ordinary space, explaining the second quantization postulates. The theory offers the explanation for the observed properties of fermion and bosons and for several cosmological observations. Since the number of creation and annihilation operators for fermions and bosons is in this theory the same, manifesting correspondingly a kind of supersymmetry, the authors start to study in this contribution the properties of the creation and annihilation operators if extending the point fermions and bosons into strings, expecting that this theory offers the low energy limit for the {\it string theory}.Comment: 23 pages, 2 figures, Bled workshops, ISSN1580-4992, DOI. 10.51746/9789612972097. arXiv admin note: substantial text overlap with arXiv:2306.17167, arXiv:2210.07004, arXiv:2210.0625