Related papers: Noncommutative spin-1/2 representations
The conformal limit over an anti-ferromagnetic vacuum of the fermionic spin $\frac{1}{2}$ Calogero-Sutherland Model is derived by using the wedge product formalism. The space of states in the conformal limit is identified with the Fock…
We propose method for studying relativistic spin-$1/2$ particles by solving the corresponding Feshbach-Villars equation. We have found that the Feshbach-Villars spin-$1/2$ equations can be formulated as spin-coupled Feshbach-Villars…
We address the non-binary coupling of identical angular momenta based upon the representation theory for the symmetric group. A correspondence is pointed out between the complete set of commuting operators and the reference-frame-free…
We study spin-1/2 fermions in spin dependent potentials under the \emph{spin model approximation}, in which interatomic collisions that change the total occupation of single-particle modes are ignored. The spin model approximation maps the…
Two Non-Hermitian fermion models are proposed and analyzed by using Foldy-Wouthuysen transformations. One model has Lorentz symmetry breaking and the other has a non-Hermitian mass term. It is shown that each model has real energies in a…
We present a first-quantized formulation of the quadratic non-commutative field theory in the background of abelian (gauge) field. Even in this simple case the Hamiltonian of a propagating particle depends non-trivially on the momentum…
In a previous work [arXiv1905.01121] we have derived a quantum master equation for the dynamics of a scalar bosonic particle interacting with a weak, stochastic and classical gravitational field. As standard matter is made of fermions, such…
We report three manifestly Lorentz-invariant Hamiltonian formulations of minimally and nonminimally coupled fermion fields to the Holst action. These formulations are achieved by making a suitable parametrization of both the tetrad and the…
Throughout this paper $A$ is a commutative non-associative algebra over a field $\mathbb{F}$ of characteristic not $2.$ In addition $A$ posses a Frobenius form. We obtain detailed information about the multiplication in $A$ given two axes…
We show that under the operation of parity the {\it front-form} $(1/2,\,0)$ and $(0,\,1/2)$ Weyl spinors (massive or massless) do not get interchanged. This has the important consequence that if a front-form theory containing…
We study the influence of the quadratic Zeeman effect in the Mott-insulator phases of hard-core spin-3/2 fermions. We show that contrary to spinor bosons, any quadratic Zeeman coupling preserves a $SU(2)\otimes SU(2)$ symmetry, leading for…
An evolution equation for the expectation values of the Boltzmann factor between monomer valence bond states is derived. It contains the whole information on the thermodynamical and magnetic properties of the spin $\frac{1}{2}$ quantum…
Using the algebraic Bethe ansatz method, and the solution of the quantum inverse scattering problem for local spins, we obtain multiple integral representations of the $n$-point correlation functions of the XXZ Heisenberg spin-$1 \over 2$…
We establish the theoretical foundation of the Wigner superposition field, a quantum field framework for spin-1/2 fermions that exhibit a Wigner doublet -- a discrete quantum number arising from nontrivial representations of the extended…
We show that several Hamiltonians that are $\mathcal{PT}$ symmetric may be taken to Hermitian Hamiltonians via a non-unitary transformation and vice versa. We also show that for some specific Hamiltonians such non-unitary transformations…
We study a class of representations of the Cuntz algebras O_N, N=2,3,..., acting on L^2(T) where T=R/2\pi Z. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into…
Using the theory of signatures of hermitian forms over algebras with involution, developed by us in earlier work, we introduce a notion of positivity for symmetric elements and prove a noncommutative analogue of Artin's solution to…
Based on the Dirac spinor representation of the SO(4) group, we discuss the relationship between three types of representation of spin in terms of Majorana fermions, namely the Kitaev representation, the SO(3) representation and the SO(4)…
By exploiting the freedom in defining the dual of spinors, we report an unexpected theoretical discovery of a quantum field theory of spin-half bosons. It fulfils Dirac's 1969-70 observation that "there must be boson variables connected…
We use the exact determinantal representation derived by Kitanine, Maillet, and Terras for matrix elements of local spin operators between Bethe wave functions of the one-dimensional s=1/2 Heisenberg model to calculate and numerically…