293,132 research outputs found
Algebraic models of hadron structure: I. Nonstrange baryons
We introduce an algebraic framework for the description of baryons. Within
this framework we study a collective string-like model and show that this model
gives a good overall description of the presently available data. We discuss in
particular masses and electromagnetic couplings, including the transition form
factors that can be measured at new electron facilities.Comment: to be published in Annals of Physics (N.Y.), 44 pages of LaTex, 11
postscript figure files on request, UU-94-0
Hubbard Models as Fusion Products of Free Fermions
A class of recently introduced su(n) `free-fermion' models has recently been
used to construct generalized Hubbard models. I derive an algebra defining the
`free-fermion' models and give new classes of solutions. I then introduce a
conjugation matrix and give a new and simple proof of the corresponding
decorated Yang-Baxter equation. This provides the algebraic tools required to
couple in an integrable way two copies of free-fermion models. Complete
integrability of the resulting Hubbard-like models is shown by exhibiting their
L and R matrices. Local symmetries of the models are discussed. The
diagonalization of the free-fermion models is carried out using the algebraic
Bethe Ansatz.Comment: 14 pages, LaTeX. Minor modification
Tensor models and 3-ary algebras
Tensor models are the generalization of matrix models, and are studied as
models of quantum gravity in general dimensions. In this paper, I discuss the
algebraic structure in the fuzzy space interpretation of the tensor models
which have a tensor with three indices as its only dynamical variable. The
algebraic structure is studied mainly from the perspective of 3-ary algebras.
It is shown that the tensor models have algebraic expressions, and that their
symmetries are represented by 3-ary algebras. It is also shown that the 3-ary
algebras of coordinates, which appear in the nonassociative fuzzy flat
spacetimes corresponding to a certain class of configurations with Gaussian
functions in the tensor models, form Lie triple systems, and the associated Lie
algebras are shown to agree with those of the Snyder's noncommutative
spacetimes. The Poincare transformations on the fuzzy flat spacetimes are shown
to be generated by 3-ary algebras.Comment: 21 pages, no essential changes of contents, but explanations added
for clarit
Holomorphic matrix models
This is a study of holomorphic matrix models, the matrix models which
underlie the conjecture of Dijkgraaf and Vafa. I first give a systematic
description of the holomorphic one-matrix model. After discussing its
convergence sectors, I show that certain puzzles related to its perturbative
expansion admit a simple resolution in the holomorphic set-up. Constructing a
`complex' microcanonical ensemble, I check that the basic requirements of the
conjecture (in particular, the special geometry relations involving chemical
potentials) hold in the absence of the hermicity constraint. I also show that
planar solutions of the holomorphic model probe the entire moduli space of the
associated algebraic curve. Finally, I give a brief discussion of holomorphic
models, focusing on the example of the quiver, for which I extract
explicitly the relevant Riemann surface. In this case, use of the holomorphic
model is crucial, since the Hermitian approach and its attending regularization
would lead to a singular algebraic curve, thus contradicting the requirements
of the conjecture. In particular, I show how an appropriate regularization of
the holomorphic model produces the desired smooth Riemann surface in the
limit when the regulator is removed, and that this limit can be described as a
statistical ensemble of `reduced' holomorphic models.Comment: 45 pages, reference adde
From Quantum to Trigonometric Model: Space-of-Orbits View
A number of affine-Weyl-invariant integrable and exactly-solvable quantum
models with trigonometric potentials is considered in the space of invariants
(the space of orbits). These models are completely-integrable and admit extra
particular integrals. All of them are characterized by (i) a number of
polynomial eigenfunctions and quadratic in quantum numbers eigenvalues for
exactly-solvable cases, (ii) a factorization property for eigenfunctions, (iii)
a rational form of the potential and the polynomial entries of the metric in
the Laplace-Beltrami operator in terms of affine-Weyl (exponential) invariants
(the same holds for rational models when polynomial invariants are used instead
of exponential ones), they admit (iv) an algebraic form of the gauge-rotated
Hamiltonian in the exponential invariants (in the space of orbits) and (v) a
hidden algebraic structure. A hidden algebraic structure for
(A-B-C{-D)-models, both rational and trigonometric, is related to the
universal enveloping algebra . For the exceptional -models,
new, infinite-dimensional, finitely-generated algebras of differential
operators occur. Special attention is given to the one-dimensional model with
symmetry. In particular, the origin
of the so-called TTW model is revealed. This has led to a new quasi-exactly
solvable model on the plane with the hidden algebra .Comment: arXiv admin note: substantial text overlap with arXiv:1106.501
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