Spectral action on a fuzzy sphere
In this paper, the spectral action for the free Dirac operator on a fuzzy 2-sphere is considered, based on the known results. We show that from the spectral point of view, the behavior of the fuzzy sphere can be divided into three regimes: the classical regime, the quasi-classical regime and the fuzzy regime. We also consider its application to quantum cosmology.

title: Bosonic Realization of Boundary Operators in SU(2)-invariant Thirring Model
abstract: Boundary operators and boundary states in the SU(2)-invariant Thirring model are considered from the point of view of bosonization and oscillator realizations of bulk and boundary Zamolodchikov-Faddeev algebras.

title: Solitons in non-left-right symmetric conformal integrable Toda fields
abstract: One- and two-soliton solutions in non-left-right symmetric conformal integrable Toda fields are obtained using the Hirota method.

title: Geometrical quantities on a fuzzy sphere
abstract: In this paper, we consider the geometrical quantities on the fuzzy sphere from the spectral point of view, such as the area and the dimension. We find that, in contract to the standard sphere, the area and the dimension are the functions of the energy scale of the fuzzy sphere.

title: False vacuum decay in generalized extended inflation
abstract: We study false-vacuum decay in context of generalized extended inflationary theories, and compute the bubble nucleation rates for these theories in the limit of G N → 0. We find that the time dependence of the nucleation rate can be exponentially strong through the time dependence of the Jordan—Brans—Dicke field. This can have a pronounced effect on whether extended inflation can be successfully implemented.

title: Quantum Wave Equation of Photon
abstract: In this paper, we give the quantum wave equations of single photon when it is in the vacuum and medium. With these wave equations, we can study light interference and diffraction with the approach of quantum theory, and also can study the quantum property of photon when it is in a general crystal and photonic crystal. Otherwise, it can be applied in quantum optics and condensed matter feld.

title: Solution Transformations for GS String in AdS_5 x S^5 by Conserved Quantities
abstract: For Light-cone gauge of Green-Schwarz superstring in AdS_5 x S^5 background, we fix two bosonic variables x^{+}=\tau and y^{9}=\sigma, and then perform the partial Legendre transformation of the remaining bosonic variables. We then obtain a Lagrangian which is linear in velocity after eliminating the metric of world sheet. For such a system, one can formulate its poisson bracket and Hamiltonian. Since this system is free and without constraint, the hierarchy of infinite nonlocal conserved quantities given by Bena, Polchinski and Roiban, induce solution transformations due to Jacobi identity.

title: Eternal Inflation: Prohibited by Quantum Gravity?
abstract: We investigate how eternal inflation is affected by quantum gravity effects. We consider general features of quantum gravity, such as renormalizability, complementarity, minimal length, definition of observables, and weak gravity conjecture. We also consider phenomenological models such as ghost inflation, non-commutative inflation, brane inflation, k-inflation and resonant tunneling. We find that all these features and models do not support eternal inflation. These evidences show hints that eternal inflation is prohibited by quantum gravity.

title: Planck priors for dark energy surveys
abstract: Although cosmic microwave background anisotropy data alone cannot constrain simultaneously the spatial curvature and the equation of state of dark energy, CMB data provide a valuable addition to other experimental results. However computing a full CMB power spectrum with a Boltzmann code is quite slow; for instance if we want to work with many dark energy and/or modified gravity models, or would like to optimize experiments where many different configurations need to be tested, it is possible to adopt a quicker and more efficient approach. In this paper we consider the compression of the projected Planck cosmic microwave background data into four parameters, R (scaled distance to last scattering surface), l{sub a} (angular scale of sound horizon at last scattering), {omega}{sub b}h{sup 2} (baryon density fraction) and n{sub s} (powerlaw index of primordial matter power spectrum), all of which can be computed quickly. We show that, although this compression loses information compared to the full likelihood, such information loss becomes negligible when more data is added. We also demonstrate that the method can be used for canonical scalar-field dark energy independently of the parametrization of the equation of state, and discuss how this method should be used for other kindsmore » of dark energy models.« less