Related papers: A Mapping between the Spin and Fermion Algebra
We develop a general formalism of duality rotations for bosonic conformal spin-$s$ gauge fields, with $s\geq 2$, in a conformally flat four-dimensional spacetime. In the $s=1$ case this formalism is equivalent to the theory of…
In a recent paper, we described a lifting of coordinate rings of groups, loops, quantum groups, etc. to the categoric setup of operads. In most examples of that paper, these rings are non--commutative. Quantum physics of the XX--th century…
The non-perturbative constraints imposed by intrinsic fermionic non-invertible symmetries in 1+1 dimensional gapped systems remain largely unexplored. In this letter, we propose the superstrip algebra as a unified framework to catalog the…
We consider the class of quantum spin chains with arbitrary $U_q(\mathfrak{sl}_2)$-invariant nearest neighbor interactions, sometimes called $\textrm{SU}_q(2)$ for the quantum deformation of $\textrm{SU}(2)$, for $q>0$. We derive sufficient…
Fermionic Gaussian operators are foundational tools in quantum many-body theory, numerical simulation of fermionic dynamics, and fermionic linear optics. While their structure is fully determined by two-point correlations, evaluating their…
We study higher spin (pure and mixed spin) representations of the Yangian of $\mathfrak{sl}_2$. We provide a geometric realization in terms of the critical cohomology of representations of the quiver with potential of Bykov and Zinn-Justin…
We report on the status of our programme to simulate Sp($2N$) gauge theories on the lattice. Motivated by the potential realization of an SU($4$)/Sp($4$)$\sim$SO($6$)/SO($5$) composite Higgs model and the applications to self interacting…
We consider a class of (possibly nondiagonalizable) pseudo-Hermitian operators with discrete spectrum, showing that in no case (unless they are diagonalizable and have a real spectrum) they are Hermitian with respect to a semidefinite inner…
The similarity renormalization group is used to transform Dirac Hamiltonian into a diagonal form, which the upper (lower) diagonal element becomes an operator describing Dirac (anti-)particle. The eigenvalues of the operator are verfied to…
This paper is the completion of an earlier work arXiv:1207.4867 which involves the derivation of oblique corrections in the MSSM at one loop. In terms of the two-component spinor formalism, which is new in compared with those used in the…
We study the $SU(2)_k/U(1)$-parafermion model perturbed by its first thermal operator. By formulating the theory in terms of a (perturbed) fermionic coset model we show that the model is equivalent to interacting WZW fields modulo free…
Following the Schwinger boson representation for the su(M+1)- and the su(N,1)-algebra presented by two of the present authors (J. da P. and M. Y.) and Kuriyama, a possible counterpart of the Lipkin model in the su(M+1)-algebra formulated in…
A categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2) was constructed in the paper arXiv:0803.3652 by the second author. Here we enhance the graphical calculus introduced and developed in that paper to include…
The classical superconformal actions of branes in adS superspaces have a closed form depending on a matrix $M^2$ quadratic in fermions, as found in hep-th/9805217. One can gauge-fix the local $\kappa$-symmetry using the Killing spinors of…
We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin characters evaluated on a strict partition $\xi$…
All possible permutations in the discrete $S_4$ group are classified by three rotation angles associated with the orthogonal group $O(3)$. We construct a spinor representation ${\bf 2}_D$ of $O(3)$, which is transformed by three 4$\times$4…
The Green function of the quark-antiquark system in the confining background field is analysed using the Feynman-Schwinger formalism. The Hamiltonian for the case of massive spinning quarks is obtained in the form containing essentially…
The spin-statistics conection is obtained for classical point particles. The connection holds within pseudomechanics, a theory of particle motion that extends classical physics to include anticommuting Grassmann variables, and which…
A $\gamma$-deformed version of $su(2)$ algebra with non-hermitian generators has been obtained from a bi-orthogonal system of vectors in $\bf{C^2}$. The related Jordan-Schwinger(J-S) map is combined with boson algebras to obtain a hierarchy…
We study the 1-dimensional Heisenberg antiferromagnet with s=1/2 using a Majorana representation of the s=1/2 spins. A simple Hartree-Fock approximation of the resulting model gives a bilinear fermionic description of the model. This…