Optimal transport by omni-potential flow and cosmological reconstruction

Uriel Frisch, Olga Podvigina, Barbara Villone, and Vladislav Zheligovsky

Using a WKB technique, it is shown that in two dimensions, for sufficiently short times, there are omni-potential flows with arbitrary smooth initial velocity. The authors argue that the results have important implications for the problem of reconstructing the dynamical history of the universe from the knowledge of the present mass distribution.

J. Math. Phys. 53, 033703 (2012)

Mixed initial-boundary value problem for intermediate long-wave equation

Elena I. Kaikina

The author considers the inhomogeneous mixed problem for the intermediate long-wave (ILW) equation on the half-line to obtain global in time existence of solutions and the asymptotic behavior of solutions for large time. It is expected that the method developed is applicable to a wide class of dispersive nonlinear nonlocal equations.

J. Math. Phys. 53, 033701 (2012)

A fifth order differential equation for charged perfect fluids

M. C. Kweyama, K. S. Govinder, and S. D. Maharaj

Utilizing a generalized transformation, the authors reduced the system of Einstein-Maxwell field equations to a single nonlinear second order partial differential equation modeling the behavior of spherically symmetric charged fluids. A fifth order purely differential equation was derived for the existence of a Lie point symmetry.

J. Math. Phys. 53, 033707 (2012)

Quantum deformation of two four-dimensional spin foam models

Winston J. Fairbairn and Catherine Meusburger

The authors construct the q-deformed spin foam models corresponding to the Lorentzian and Euclidean EPRL (Engle, Pereira, Rovelli and Livine) models. For the two four-dimensional spin foam models, the authors provide a definition of the quantum EPRL intertwiners, study their convergence and braiding properties, and construct an amplitude for the four-simplexes.

J. Math. Phys. 53, 022501 (2012)

Spinor representation for loop quantum gravity

Etera Livine and Johannes Tambornino

By rigorously expanding the recently developed spinorial formulation of loop gravity to the quantum theory, the authors show the unitary equivalence between the resulting generalized Bargmann space and the standard loop quantum gravity Hilbert space with an explicitly constructed unitary map. In addition, the authors argue that the unitary map provides a tool to efficiently calculate physical quantities since integrals over the group are exchanged for straightforward integrals over the complex plane.

J. Math. Phys. 53, 012503 (2012)