Related papers: Essential Fierz identities for a fermionic field
For the description of space-time fermions, Dirac-K\"ahler fields (inhomogeneous differential forms) provide an interesting alternative to the Dirac spinor fields. In this paper we develop a similar concept within the symplectic geometry of…
We emphasize that the group-theoretical considerations leading to SO(10) unification of electro-weak and strong matter field components naturally extend to space-time components, providing a truly unified description of all generation…
We consider a Dirac field in 2+1 Euclidean dimensions, in the presence of a linear domain wall defect in its mass, and a constant electromagnetic field. We evaluate the exact fermionic determinant for the situation where the defect is…
It is well-known that macroscopically-normalizable zero-energy wavefunctions of spin-$\frac{1}{2}$ particles in a two-dimensional inhomogeneous magnetic field are spin-polarized and exactly calculable with degeneracy equaling the number of…
Real Clifford algebras for arbitrary number of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed. The Clifford algebras are classified in terms of isomorphic matrix algebras of real,…
A new aspect of the vacuum structure of 2+1-dimensional Thirring model is presented. Using the Fierz identity, we split the current-current four-Fermi interaction in terms of a matrix valued auxiliary scalar field and compute its effective…
A cubic identity for the Infeld-van der Waerden field is found and its application to verifying an explicit formula for the spinor components of the metric connection is demonstrated.
The Euclidean fermionic determinant in four-dimensional quantum electrodynamics is considered as a function of the fermionic mass for a class of $O(2)\times O(3)$ symmetric background gauge fields. These fields result in a determinant free…
We study an effective field theory which includes the Standard Model extended by a Dark Sector consisting of two fermionic $SU(2)_{L}$-doublets. A $Z_2$ parity guarantees that, after electroweak symmetry breaking, the lightest neutral…
We construct the higher-spin massive fermionic fields in 2+1 dimensions. Their field equations and propagators are derived from first principle. For fields with j>1/2, complications arise from the non-linear behaviour of the boost…
An exact representation of the Euclidean fermion determinant in two dimensions for centrally symmetric, finite-ranged Abelian background fields is derived. Input data are the wave function inside the field's range and the scattering phase…
All independent interaction vertices involving massless (Fang--Fronsdal) fermions in three dimensions are classified, completing the classification of interactions of massless fields of any spin. Similarly to the bosonic case, we get no…
The Lounesto classification splits spinors in six classes: I, II, III are those for which at least one among scalar and pseudo-scalar bi-linear spinor quantities is non-zero, its spinors are called regular, and among them we find the usual…
This work deals with new classes of spinors of mass dimension one in Minkowski spacetime. In order to accomplish it, the Lounesto classification scheme and the inversion theorem are going to be used. The algebraic framework shall be…
We study f(R)-gravity with torsion in presence of Dirac massive fields. Using the Bianchi identities, we formulate the conservation laws of the theory and we check the consistency with the matter field equations. Further, we decompose the…
We propose the creation and investigation of a system of spin-one fermions in the presence of artificial spin-orbit coupling, via the interaction of three hyperfine states of fermionic atoms to Raman laser fields. We explore the emergence…
To describe external and internal attributes of fundamental fermions, a theory of multi-spinor fields is developed on an algebra, a {\it triplet algebra}, which consists of all the triple-direct-products of Dirac \gamma-matrices. The…
Transition probability calculations of strong field particle processes in the Furry picture, typically use fermion Volkov solutions. These solutions have a relatively complicated spinor due to the interaction of the electron spin with a…
We define Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups $\Gamma_\vartheta$, $\Gamma^0(2)$ and $\Gamma_0(2)$ of $\text{SL}_2(\mathbb Z)$. Each subgroup corresponds to one of the spin structures on the…
We suggest model equations, which, from some point of view, describe local interaction of three physical fields: a field of matter, an electromagnetic field and a gravitational field. A base of the model is a field of matter described by…