Related papers: Non-standard Schwinger fermionic representation of…
Based on the superconformal algebra we construct a dual operator that introduces a grading among bosonic generators independent of the boson/fermion grading of the superalgebra. This dual operator allows us to construct an action that is…
A direct consequence of the occurrence of fermion families is the invariance of currents under certain groups of (universality) transformations. We show how these universality groups can themselves be used to find and study grand family…
Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically…
We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a…
We represent the generators of the SU(N) algebra as bilinear combinations of Fermi operators with imaginary chemical potential. The distribution function, consisting of a minimal set of discrete imaginary chemical potentials, is found for…
We analyze the structure of the group of (local) non-linear canonical transformations that exist in a system with n fermionic modes. To perform our study we develop an alternative framework to represent the generators of these canonical…
With the usual definition of a super Hilbert space and a super unitary representation, it is easy to show that there are lots of super Lie groups for which the left-regular representation is not super unitary. I will argue that weakening…
Noncommutative Yang-Mills theories are sensitive to the choice of the representation that enters in the gauge kinetic term. We constrain this ambiguity by considering grand unified theories. We find that at first order in the…
Superbosonization is a new variant of the method of commuting and anti-commuting variables as used in studying random matrix models of disordered and chaotic quantum systems. We here give a concise mathematical exposition of the key…
The boundary operator is a linear operator that acts on a collection of high-dimensional binary points (simplices) and maps them to their boundaries. This boundary map is one of the key components in numerous applications, including…
The axial anomaly arising from the fermion sector of $\U(N)$ or $\SU(N)$ reduced model is studied under a certain restriction of gauge field configurations (the ``$\U(1)$ embedding'' with $N=L^d$). We use the overlap-Dirac operator and…
We present calculations of certain limits of scheme-independent series expansions for the anomalous dimensions of gauge-invariant fermion bilinear operators and for the derivative of the beta function at an infrared fixed point in SU($N_c$)…
The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C^n tensor C^n whose operator-Schmidt decompositions…
We consider non-supersymmetric quiver theories obtained by orbifolding the N=4 supersymmetric U(K) gauge theory by a discrete Z_\Gamma group embedded in the SU(4) R-symmetry group. We explicitly find that in such theories there are no…
In this work we uncover the mathematical structure of the Schwinger algebra and introduce an almost unitary Schwinger operators which are derived by considering translation operators on a finite lattice. We calculate mathematical relations…
In the conventional formulation of N=1 supersymmetry, a vector multiplet is supposed to be in the adjoint representation of a given gauge group. We present a new formulation with a vector multiplet in the non-adjoint representation of SO(N)…
It is known that local operators in quantum field theory transform in representations of ordinary global symmetry groups. The purpose of this paper is to generalise this statement to extended operators such as line and surface defects. We…
In this article we construct Weil representations of quasi-split unitary groups $U(n,n)(\mathbb{F}_{q^2}/\mathbb{F}_q)$ associated to quadratic extensions of finite fields. We define these representations by using an adequate presentation…
A new representation for electrons is introduced, in which the electron operators are written in terms of a spinless fermion and the Pauli operators. This representation is canonical, invertible and constraint-free. Importantly, it…
We give two explicit construction for the carrier space for the Schwinger representation of the group $S_n$. While the first relies on a class of functions consisting of monomials in antisymmetric variables, the second is based on the Fock…