We discuss the application of the permutation group SN to a few problems in hadron physics. In Ref. [11] a method was proposed for matching a quark model Hamiltonian onto the effective Hamiltonian of the 1/Nc expansion, which makes use of the transformation properties of the states and operators under SN . This method is used in [13] to obtain information about the spinflavor structure of the q...

We briefly discuss the state of the art on the anomalous dynamics of the Hamiltonian Mean Field model. We stress the important role of the initial conditions for understanding the microscopic nature of the intriguing metastable quasi stationary states observed in the model and the connections to Tsallis statistics and glassy dynamics. We also present new results on the existence of metastable s...

We study the question of diagonalizability of the Hamiltonian for the FaddeevReshetikhin (FR) model in the two particle sector. Although the two particle S-matrix element for the FR model, which may be relevant for the quantization of strings on AdS5×S, has been calculated recently using field theoretic methods, we find that the Hamiltonian for the system in this sector is not diagonalizable. W...

We apply the subtraction method to an effective QCD-inspired model, which includes the Coulomb plus a zerorange hyperfine interactions, to define a renormalized Hamiltonian for mesons. The spectrum of the renormalized Hamiltonian agrees with the one obtained with a smeared hyperfine interaction. The masses of the low-lying pseudo scalar and vector mesons are reasonably described within the model.

We analyze the Hamiltonian of the compactified D = 11 supermembrane with non-trivial central charge in terms of the matrix model constructed in [1]. Our main result provides a rigorous proof that the quantum Hamiltonian of the supersymmetric model has compact resolvent and thus its spectrum consists of a discrete set of eigenvalues with finite multiplicity.

We study a simple quantized model for which perturbation theory gives ultravioletly divergent results. We show that when the eigen-solution problem of the Hamiltonian of the model is treated nonperturbatively, it is possible for eigenenergies of the Hamiltonian to be finite. PACS number: 11.15 Tk Typeset using REVTEX 1

1 The Ising Model The Ising Model is a simple model of a solid that exhibits a phase transition resembling ferromagnetism. In this model, a “spin direction” is assigned to each vertex on a graph. The standard Hamiltonian for an Ising system includes only nearest-neighbor interactions and each spin direction may be either “up” (+1) or “down” (-1), though generalized models may include long-range...

The Hamiltonian of the Rabi model is considered. It is shown in the light of quantum phase transition that the ground state energy of the Rabi Hamiltonian does not cross any other energies.

We show that Gutzwiller’s characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian can be extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model when a transition i...

We introduce a class of exactly solvable boson models. We give explicit analytic expressions for energy eigenvalues and eigenvectors for an sd-boson Hamiltonian, which is related to the SO(6) chain of the Interacting Boson Model Hamiltonian.