Non-linear Fourier analysis on compact groups is used to construct an orthonormal basis of the physical (gauge invariant) Hilbert space of Hamiltonian lattice gauge theories. In particular, the matrix elements of the Hamiltonian operator involved are explicitly computed. Finally, some applications and possible developments of the formalism are discussed. CPT-99/P.3856 University of Parma Prepri...

We propose a geometric setting for the Hamiltonian description of mechanical systems with a nonholonomic constraint, which may be used for constraints of general type (non-linear in the velocities, and such that the constraint forces may not obey Chetaev's rule). Such constraints may be realized by servomechanisms; therefore, the corresponding mechanical system may be nonconservative. In that s...

The anomalous dimensions of local single trace gauge invariant operators in N = 4 supersymmetric Yang-Mills theory can be computed by diagonalizing a long range integrable Hamiltonian by means of a perturbative asymptotic Bethe ansatz. This formalism breaks down when the number of fields of the composite operator is smaller than the range of the Hamiltonian which coincides with the order in per...

We study Hamiltonian stationary Lagrangian surfaces in C, i.e. Lagrangian surfaces in C which are stationary points of the area functional under smooth Hamiltonian variations. Using loop groups, we propose a formulation of the equation as a completely integrable system. We construct a Weierstrass type representation and produce all tori through either the integrable systems machinery or more di...

In this exposition we investigate further the methodology developed in [Mo2] to study properties of the ground states of a translation invariant Hamiltonian for one lattice dimensional quantum spin chain A = ⊗ZZMd, where Md is the space of d × d complex matrices. To that end we study the associated Cuntz elements [Mo2] representing a translation invariant pure state and find an useful criteria ...

Abstract. Xu introduced a class of nongraded Hamiltonian Lie algebras. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a “sandwich” method and by studying some features of these Lie algebras. It is obtained that two Hamiltonian Lie algebras are isomorphic if and only if their corresponding Poisson alge...

  The traveling salesman problem is a well-known and important combinatorial optimization problem. The goal of this problem is to find the shortest Hamiltonian path that visits each city in a given list exactly once and then returns to the starting city. In this paper, for the first time, the shortest Hamiltonian path is achieved for 1071 Iranian cities. For solving this large-scale problem, tw...

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...