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Non-Abelian family symmetries offer a very promising explanation for the flavour structure in the Standard Model and its extensions. We explore the possibility that dark matter consists in fermions that transform under a family symmetry,…
The nonbaryonic dark matter of the Universe is assumed to consist of new stable forms of matter. Their stability reflects symmetry of micro world and particle candidates for cosmological dark matter are the lightest particles that bear new…
In this survey article, we explain a few ideas behind the fermionic projector approach and summarize recent results which clarify the connection to quantum field theory. The fermionic projector is introduced, which describes the physical…
The spin-charge-family theory, which is a kind of the Kaluza-Klein theories in $d=(13+1)$ --- but with the two kinds of the spin connection fields, the gauge fields of the two Clifford algebra objects, $S^{ab}$ and $\tilde{S}^{ab}$ ---…
We extend the standard model with two iso-singlet color triplet scalars, one singlet real scalar and one singlet fermion. The new fields are odd under an unbroken Z_2 discrete symmetry while the standard model particles are even. The decays…
We present a uniform framework for the treatment of a large class of toy models of quantum theory. Specifically, we will be interested in theories of wavefunctions valued in commutative involutive semirings, and which give rise to some…
We review the derivation of light-cone interaction vertices for fermionic and bosonic fields of arbitrary spin. The resulting amplitudes and their factorization properties are discussed. We then show how this symmetry-based approach works…
The model of creation of observable particles and particles of the dark matter, considered to be superheavy particles, due to particle creation by the gravitational field of the Friedmann model of the early Universe is given. Estimates on…
We construct a quantum theory of free fermion field based on the generalized uncertainty principle using supersymmetry as a guiding principle. A supersymmetric field theory with a real scalar field and a Majorana fermion field is given…
The Dirac theory implies the existence of an internal vector space, in addition to spin space. Using Dirac's coupling of variables in internal space to those in physical space, we construct a new configuration structure for particles in the…
A composite model of the fundamental fermions based on colour preons is discussed. It is found that, if endowed with the pairwise (repulsive/attractive) chromoelectric fields, preons would cohere in a series of structures, resembling by…
We study a connection between duality and topological field theories. First, 2d Kramers-Wannier duality is formulated as a simple 3d topological claim (more or less Poincar\'e duality), and a similar formulation is given for…
The realistic free fermionic models have had remarkable success in providing plausible explanations for various properties of the Standard Model which include the natural appearance of three generations, the explanation of the heavy top…
SO(10) grand unified theories can ensure the stability of new particles in terms of the gauge group structure itself, and in this respect are well suited to accommodate dark matter (DM) candidates in the form of new stable massive…
Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. But the spin group is not the only subgroup of the Clifford algebra. An algebraist's perspective on…
In grand unified theories with gauge groups larger than SU(5), the multiplets that contain the known quarks and leptons also contain fermions that are singlets under the Standard Model gauge group. Some of these could be the dark matter of…
Some time ago it was suggested that dark matter may consist in part of an extremely dilute gas of supermassive gravitinos with fractional charge 2$e$/3 \cite{MeissnerNicolai2019}. This scheme makes the definite (and falsifiable) prediction…
It is possible to describe fermionic phases of matter and spin-topological field theories in 2+1d in terms of bosonic "shadow" theories, which are obtained from the original theory by "gauging fermionic parity". The fermionic/spin theories…
Dark matter is, arguably, the most widely discussed topic in contemporary particle physics. Written in the language of particle physics and quantum field theory, these notes focus on a set of standard calculations needed to understand…
Using parafermionic field theoretical methods, the fundamentals of 2d fractional supersymmetry ${\bf Q}^{K} =P$ are set up. Known difficulties induced by methods based on the $U_{q}(sl(2))$ quantum group representations and non commutative…