Modern Physics Letters A

We consider the effect of matter in the anisotropic universe of the scalar–tensor theory. We study Brans–Dicke model as a scalar–tensor theory. The matter is treated as perfect fluid type one. Just as the spacetime is anisotropic, the matter is also considered to be anisotropic. In order to give the present universe which is isotropic, the spacetime should be filled with the particular type of matter.

We address an old problem in lattice gauge theory — the computation of the spectrum and wave functions of excited states. Our method is based on the Hamiltonian formulation of lattice gauge theory. Using the method of Monte Carlo with importance sampling, we construct a stochastic basis of Bargmann link states, drawn from a physical probability density function. In the next step, we compute transition amplitudes between stochastic basis states. Then, we extract energy spectra and wave functions from a matrix of transition elements. To test this method, we apply it to U(1) lattice gauge theory in (2+1) dimensions and compute the energy spectrum, wave functions and thermodynamic functions of the electric Hamiltonian of this theory. We compare the numerical results with the analytical results and observe a reasonable scaling of energies and wave functions in the variable of time.

In this short note we construct a simple cut-and-join operator representation for Kontsevich–Witten tau-function that is the partition function of the two-dimensional topological gravity. Our derivation is based on the Virasoro constraints. Possible applications of the obtained representation are discussed.

Z′ boson vector and axial vector couplings to fermions are studied in terms of anomaly cancellation in the condition of small Z–Z′ mixing. The anomaly-free U(1)′ charge assignment that parametrized by two independent charges is proposed. Z′ decay width to fermion pair , hadron-to-lepton ratio , hadron branching ratio , left–right asymmetry and forward–backward asymmetry are investigated. A special sum rule of Z′ decay widths is also derived.

It is shown that the noncommutativity in quantum Hall system may get modified. The self-adjoint extension of the corresponding Hamiltonian leads to a family of noncommutative geometry labeled by the self-adjoint extension parameters. We explicitly perform an exact calculation using a singular interaction and show that, when projected to a certain Landau level, the emergent noncommutative geometries of the projected coordinates belong to a one-parameter family. There is a possibility of obtaining the filling fraction of fractional quantum Hall effect by suitably choosing the value of the self-adjoint extension parameter.