Related papers: Spin(9) Average of SU(N) Matrix Models I. Hamilton…

In this paper we give a Casimir Invariant for the Symmetric group $S_n$. Furthermore we obtain and present, for the first time in the literature, explicit formulas for the matrices of the standard representation in terms of the matrices of…

This chapter of the proceedings for the Ninth Meeting on CPT and Lorentz Symmetry is dedicated to the Hamiltonian formulation of the minimal gravitational Standard-Model Extension. Some theoretical questions associated with the latter shall…

The spin chains originating from large-N conformal gauge theories are of a special kind: The Hamiltonian is not invariant under the symmetry algebra, it is rather a part of it. This leads to interesting properties within the asymptotic…

The spectral statistics and entanglement within the eigenstates of generic spin chain Hamiltonians are analysed. A class of random matrix ensembles is defined which include the most general nearest-neighbour qubit chain Hamiltonians. For…

For a Spin(9)-structure on a Riemannian manifold M^16 we write explicitly the matrix psi of its K\"ahler 2-forms and the canonical 8-form Phi. We then prove that Phi coincides up to a constant with the fourth coefficient of the…

We examine a dual theory of a Supersymmetric Standard Model(SSM) in terms of an $SU(3)_C$ gauge group. In this scenario, it is naturally understood that at least one quark (the top quark) should be heavy, i.e., almost the same order as the…

We reveal a dynamical SU(2) symmetry in the asymptotic description of supersymmetric matrix models. We also consider a recursive approach for determining the ground state, and point out some additional properties of the model(s).

This paper surveys some combinatorial aspects of Smith normal form, and more generally, diagonal form. The discussion includes general algebraic properties and interpretations of Smith normal form, critical groups of graphs, and Smith…

We propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution…

QCD justification of SU(m/n) supergroups are shown to provide a basis for the existence of an approximate hadronic supersymmetry. Effective Hamiltonian of the relativistic quark model is derived, leading to hadronic mass formulae in…

We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or…

We consider solutions of the 2x2 matrix Hamiltonians of the physical systems within the context of the su(2) and su(1,1) Lie algebra. Our technique is relatively simple when compared with the others and treats those Hamiltonians which can…

Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome and hard to compute, theoretical methods: (1) average Hamiltonian theory following…

Exploiting inherent symmetries is a common and effective approach to speed up the simulation of quantum systems. However, efficiently accounting for non-Abelian symmetries, such as the $SU(2)$ total-spin symmetry, remains a major challenge.…

We construct commuting transfer matrices for models describing the interaction between a single quantum spin and a single bosonic mode using the quantum inverse scattering framework. The transfer matrices are obtained from certain…

The reliable simulation of spin models is of critical importance to tackle complex optimization problems that are intractable on conventional computing machines. The recently introduced hyperspin machine, which is a network of linearly and…

We consider generalizations of the standard model (SM) which are based on the gauge symmetry $SU(n)_c\otimes SU(m)_L\otimes U(1)_N$. Although the most interesting possibilities occur when $n=3$, we will consider also the cases $n=4,5$ both…

A class of non-Hermitian quadratic su(2) Hamiltonians having an anti-linear symmetry is constructed. This is achieved by analysing the possible symmetries of such systems in terms of automorphisms of the algebra. In fact, different…

An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)-structure, in terms of the nine local symmetric involutions involved, is given. The list of explicit expressions of all the canonical forms related to…

Employing the currently discussed notion of pseudo-Hermiticity, we define a pseudo-unitary group. Further, we develop a random matrix theory which is invariant under such a group and call this ensemble of pseudo-Hermitian random matrices as…