N. S. Mankoc Borstnik

Spin connection as a superpartner of a vielbein

Abstract For a particle which lives in a d-dimensional ordinary and a d-dimensional Grassmann space and has its geodesics parametrized by an ordinary and a Grassmann parameter, a super vielbein has two terms, a superpartner of an ordinary vielbein being a spin connection, expressible with a vielbein and its derivatives. A quantized theory describes a Dirac particle in a gravitational field. There are in fact two independent types of Dirac matrices, which anticommute.

How to generate families of spinors

Using a technique [Mankoc Borstnik et al., J. Math. Phys. 43, 5782 (2002)] to construct a basis for spinors and “families” of spinors in terms of Clifford algebra objects, we define other Clifford algebra objects, which transform the state of one “family” of spinors into the state of another “family” of spinors, changing nothing but the “family” number. The proposed transformation works—as does the technique—for all dimensions and any signature and might open a path to understanding families of quarks and leptons [Mankoc Borstnik, Phys. Lett. B 292, 25 (1992); J. Math. Phys. 34, 3731 (1993); Int. J. Theor. Phys. 40, 315 (2001); Borstnik Bracic and Mankoc Borstnik, hep-ph/0301029].

Why odd-space and odd-time dimensions in even-dimensional spaces?☆

Abstract We are answering the question why 4-dimensional space has the metric 1+3 by making a general argument from a certain type of equations of motion linear in momentum for any spin (except spin zero) in any even dimension d. All known free equations of motion for non-zero spin for massless fields belong to this type of equations. Requiring Hermiticity 1 of the equations of motion operator as well as irreducibility with respect to the Lorentz group representation, we prove that only metrics with the signature corresponding to q time + ( d − q ) space dimensions with q being odd exist. Correspondingly, in four dimensional space, Nature could only make the realization of 1+3-dimensional space.

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?offers 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 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.

An example of Kaluza-Klein-like theory with boundary conditions, which lead to massless and mass protected spinors chirally coupled to gauge fields

Abstract The genuine Kaluza–Klein-like theories (with no fields in addition to gravity) have difficulties with the existence of massless spinors after the compactification of some of dimensions of space [E. Witten, Nucl. Phys. B 186 (1981) 412; E. Witten, Princeton Technical Rep. PRINT-83-1056, October 1983]. We assume a M ( 1 + 3 ) × a flat finite disk in ( 1 + 5 ) -dimensional space, with the boundary allowing spinors of only one handedness. Massless spinors then chirally couple to the corresponding background gauge gravitational field, which solves equations of motion for a free field, linear in the Riemann curvature.

Fermions with no fundamental charges call for extra dimensions

Abstract In a fundamental theory of fermions carrying only a spin and no charge and interacting accordingly only gravitationally, the requirement of mass protection excludes the possibility of dimension 4 (mod 8) as well as all odd dimensions. If more than one family in dimensions divisible by 4 is required, only dimension d = 2 (mod 4) remains as acceptable.

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 approach unifying spin and charges as the fifth family. We make a rough estimation of properties of baryons of these new family members, of their behavior 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.

Spinor states on a curved infinite disc with non-zero spin-connection fields

In the paper by Lukman et al (2011 New J. Phys. 13 103027), a step towards realistic Kaluza–Klein (like) theories was made by presenting 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 S2, and with the spin connection field, which allows such a sphere only one massless spinor state of a particular charge, coupling the spinor chirally to the corresponding Kaluza–Klein gauge field. The solutions for the massless spinor state were found for a range of spin connection fields, as well as the massive ones for a particular choice of the spin connection field. In this paper we present the massless and massive spinor states for the whole range of parameters of the spin connection field that allow only one massless solution.

Discrete symmetries in the Kaluza-Klein theories

A bstractIn theories of the Kaluza-Klein kind there are spins or total angular moments in higher dimensions which manifest as charges in the observable d = (3 + 1). The charge conjugation requirement, if following the prescription in (3 + 1), would transform any particle state out of the Dirac sea into the hole in the Dirac sea, which manifests as an anti-particle having all the spin degrees of freedom in d, except S03, the same as the corresponding particle state. This is in contradiction with what we observe for the anti-particle. In this paper we redefine the discrete symmetries so that we stay within the subgroups of the starting group of symmetries, while we require that the angular moments in higher dimensions manifest as charges in d = (3 + 1). We pay attention on spaces with even d.

Quantum Gates and Quantum Algorithms with Clifford Algebra Technique

We use the Clifford algebra technique (J. Math. Phys. 43:5782, 2002; J. Math. Phys. 44:4817, 2003), that is nilpotents and projectors which are binomials of the Clifford algebra objects γa with the property {γa,γb}+=2ηab, for representing quantum gates and quantum algorithms needed in quantum computers in a simple and an elegant way. We identify n-qubits with the 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; we pay attention also on the nonrelativistic limit. An algorithm for extracting a particular information out of a general superposition of 2n qubit states is presented. It reproduces for a particular choice of the initial state the Grover’s algorithm (Proc. 28th Annual ACM Symp. Theory Comput. 212, 1996).