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In supersymmetric extensions of the Standard Model, the observed particles come in fermion-boson pairs necessary for the realization of supersymmetry (SUSY). In spite of the expected abundance of super-partners for all the known particles,…
Following the basic idea proposed by the present authors in recent paper, a possible form of the orthogonal set for many-body system consisting of six kinds of boson operators is developed. In contrast to the recent paper, in which the…
In this paper we consider squares of pseudo-bosonic ladder operators and we use them to produce explicit examples of eigenstates of certain operators satisfying a deformed $\mathfrak{su}(1,1)$ Lie algebra. We show how these eigenstates may,…
The role of the auxiliary su(2)-algebra proposed by the present authors in the latest paper is extended. Its aim is to determine the minimum weight states completely. With the aid of scalar operators for the auxiliary algebra, new aspects…
A new supersymmetric grand unified model based on the gauge group $SU(5)\times SU(5)$ is discussed. The model has the feature that the conventional seesaw mechanism for neutrino masses is implemented using the $(15, 1)+(1,\bar{15)}$…
We study quantum systems with even numbers N of levels that are completely state-controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1)/2. These Lie algebras are smaller than the respective…
We consider an SU(2)-lattice gauge model in the tree gauge. Classically, this is a system with symmetries whose configuration space is a direct product of copies of SU(2), acted upon by diagonal inner automorphisms. We derive defining…
We study the patterns in the duality of a wide class of N=1 supersymmetric gauge theories in four dimensions. We present many new generalizations of the classic duality models of Kutasov and Schwimmer, which have themselves been generalized…
On the exterior algebra over the quantum SU(2) coming from the four dimensional bicovariant calculus \`a la Woronowicz we introduce, using sesquilinear contraction maps, a class of metrics and Hodge duality operators, and compare this…
Duality properties of the $SU(2)$ Principal Chiral Model are investigated starting from a one-parameter family of its equivalent Hamiltonian descriptions generated by a non-Abelian deformation of the cotangent space $T^*SU(2) \simeq SU(2)…
A modified interaction representation for the master field describing connected $SU(N)$-invariant Wightman's functions in the large $N$ limit of matrix fields is constructed. This construction is based on the representation of the master…
Exploiting the SU(2) Skyrmion Lagrangian with second-class constraints associated with Lagrange multiplier and collective coordinates, we convert the second-class system into the first-class one in the Batalin-Fradkin-Tyutin embedding…
Let $A=F[x,y]$ be the polynomial algebra on two variables $x,y$ over an algebraically closed field $F$ of characteristic zero. Under the Poisson bracket, $A$ is equipped with a natural Lie algebra structure. It is proven that the maximal…
Lattice simulations are used to compute the spectrum of energy levels for all angular momentum and parity quantum numbers in the SU(2)-Higgs model, with parameters chosen to match experimental data from the Higgs-W boson sector of the…
We elaborate on how to build, in a systematic fashion, two-field Abelian extensions of the Born-Infeld Lagrangian. These models realize the non-trivial duality groups that are allowed in this case, namely U(2), SU(2) and U(1)xU(1). For each…
We define the quadratic algebra su(2)_{\alpha} which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can…
By direct, elementary, considerations it is shown that the SU(2) x SO(d=2,3) invariant sector of the bosonic membrane matrix model is governed by (two, resp. three-dimensional) x^2 y^2 models
We construct SU(N) irreducible Schwinger bosons satisfying certain U(N-1) constraints which implement the symmetries of SU(N) Young tableaues. As a result all SU(N) irreducible representations are simple monomials of $(N-1)$ types of SU(N)…
Within the context of the extended bi-spinor gauge theory we describe a new off-shell realization of scalar supersymmetry (s-susy) of massless interacting fields with U(1), U(1) x SU(N) and U(1) x SU(N_1) x SU(N_2) gauge groups. S-susy acts…
Bosonization of the extended Thirring model with SU(2) symmetry in the Minkowski path integral method is discussed. We argue that it is not an easy task to bosonize such a model if we derive correctly the fermion determinant which is…