Related papers: Superalgebraic structure of Lorentz transformation…

We derive the relativistic transformation laws for the annihilation operators of the scalar field, the massive spin-1 vector field, the electromagnetic field and the spinor field. The technique developed here involves straightforward…

We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each C x /(R^3) describes an electroweak doublet. The Dirac equation has a doubler-free…

We present a theoretical framework called Lorentz quantum mechanics, where the dynamics of a system is a complex Lorentz transformation in complex Minkowski space. In contrast, in usual quantum mechanics, the dynamics is the unitary…

In this work we present symmetry transformations relating bosons to fermions which cannot be represented as a supersymmetric algebra. We present a symmetry transformation relating a complex scalar and a fermion in four dimensions and…

Dirac operators on curved space-times are introduced with the help of a new point-view that observers have to be included in the formulation of natural laws. The class of Dirac operators are Lorentz invariant in the sense that the…

Fermions are coupled to the Einstein-Cartan system in the canonical formulation, including the cosmological, the Barbero-Immirzi, and the non-minimal coupling constants. The resulting ten first-class constraints generate gauge…

Research on topological phases of matter is a core field in modern condensed matter physics. Free fermion systems, such as topological insulators and superconductors, have been studied using the "Tenfold Way" and K-theory. Building on…

We introduced fermionic variables in complex modules over real Clifford algebras of even dimension which are analog of the Witt basis. We built primitive idempotents which are a set of equivalent Clifford vacuums. It is shown that the…

A functional integral approach is developed to discuss the bosonisation of the massive Thirring and the massive Schwinger models in arbitrary D-dimensions. It is found that these models, to {\it all} orders in the inverse fermi mass,…

It is shown that the ${\cal N}=1$ supersymmetric quantum mechanics (SQM) can be extended to a $\mathbb{Z}_2^n$-graded superalgebra. This is done by presenting quantum mechanical models which realize, with the aid of Clifford gamma matrices,…

The paper concerns standard supersymmetry algebras in diverse dimensions, involving bosonic translational generators and fermionic supersymmetry generators. A cohomology related to these supersymmetry algebras, termed supersymmetry algebra…

In Ref. [arXiv:1802.05554v3] one of the authors (N.S.M.B.) studies the second quantization of fermions with integer spin while describing the internal degrees of freedom of fermions in Grassmann space. In this contribution we study the…

We introduce an antisymplectic Dirac operator and antisymplectic gamma matrices. We explore similarities between, on one hand, the Schroedinger-Lichnerowicz formula for spinor bundles in Riemannian spin geometry, which contains a…

The properties of the covariant quantum fields on de Sitter spacetimes are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary…

We give a new interpretation for the super loop space that has been used to formulate supersymmetry. The fermionic coordinates in the super loop space are identified as the odd generators of the Weil algebra. Their bosonic superpartners are…

In this paper we start from a basic notion of process, which we structure into two groupoids, one orthogonal and one symplectic. By introducing additional structure, we convert these groupoids into orthogonal and symplectic Clifford…

The mass dimension one (MDO) fermionic field is built on a complete set of dual-helicity eigenspinors of the charge conjugation operator, which obeys the statistic of Fermi-Dirac. These spinors are a potential candidate for the description…

We examine the structure of the Clifford algebra associated with a Hermitian bilinear form and apply the result to a dynamical model of the relativistic point particle. The dynamics of the particle is described by a Dirac spinor with…

We extend to a non-Hermitian fermionic quantum field theory with PT symmetry our previous discussion of second quantization, discrete symmetry transformations, and inner products in a scalar field theory [arXiv:2006.06656]. For…

We define a superalgebra S2(N/2) as a Z2 graded algebra of dimension 2N+3, where N is a positive, odd integer. The even component is a three-dimensional abelian subalgebra, while the odd component is made up of two N-dimensional, mutually…