Canonical formalism for simplicial gravity

We summarise a recently introduced general canonical formulation of discrete systems which is fully equivalent to the covariant formalism. This framework can handle varying phase space dimensions and is applied to simplicial gravity in particular.Comment: 4 pages, 5 figures, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS

Master Constraint Operator in Loop Quantum Gravity

We introduce a master constraint operator $\hat{\mathbf{M}}$ densely defined in the diffeomorphism invariant Hilbert space in loop quantum gravity, which corresponds classically to the master constraint in the programme. It is shown that $\hat{\mathbf{M}}$ is positive and symmetric, and hence has its Friedrichs self-adjoint extension. The same conclusion is tenable for an alternative master operator $\hat{\mathbf{M'}}$, whose quadratic form coincides with the one proposed by Thiemann. So the master constraint programme for loop quantum gravity can be carried out in principle by employing either of the two operators.Comment: 11 pages, significant modification in section 2, accepted for publication in Phys. Lett.

(3+1)-dimensional topological phases and self-dual quantum geometries encoded on Heegard surfaces

We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the (2+1)-dimensional Turaev-Viro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects. This work has important applications for quantum gravity as well as the theory of topological phases in (3+1) dimensions. It provides a self-dual quantum geometry realization based on a vacuum state peaked on a homogeneously curved geometry. The state spaces and operators we construct here provide also an improved version of the Walker-Wang model, and simplify its analysis considerably. We in particular show that the fusion bases of the (2+1)-dimensional theory lead to a rich set of bases for the (3+1)-dimensional theory. This includes a quantum deformed spin network basis, which in a loop quantum gravity context diagonalizes spatial geometry operators. We also obtain a dual curvature basis, that diagonalizes the Walker-Wang Hamiltonian. Furthermore, the construction presented here can be generalized to provide state spaces for the recently introduced dichromatic four-dimensional manifold invariants.Comment: 27 pages, many figures, v2: minor correction

On Schwinger's formula for pair production

We present some comments on Schwinger's calculation of electron-positron production in a prescribed constant electric field. The range of validity of 2 Im \mathcal{L}^(1)(E) is discussed thoroughly and limiting cases are provided

The Coulomb Green's Function in Two Dimensions

We consider the two-dimensional non-relativistic Coulomb problem with the aid of the momentum space construction of the associated Green's function. Our presentation has precursors in three dimensions. It is mainly Schwinger's approach which we advocate and project onto two dimensions.Comment: 20 pages, LaTe

Book review\ud Andre, J., Owens, D. A., & Harvey, Jr., L. O. (Eds.). (2003). Visual perception: The influence of H. W. Leibowitz. Washington, DC: APA.

In the edifice of visual psychology there are many mansions. This book comes from one of the finest in it.\ud The influence of Herschel Leibowitz has been immense (e.g., teaching in four languages and publishing\ud more than 250 papers) blending rigorous inquiry with inspirational teaching and dedicated public\ud service. This “Decade of Behavior” festschrift is exemplary in many respects, such as giving a readable\ud account of complicated vision problems, as bridging applied and theoretical questions, as to the\ud productiveness of cross-disciplinary collaboration, and, last but not least, to the significance of an\ud inspirational teacher, mentor, and colleague. Reading the book will give you a kind of immersion experience,\ud typical in style of the man himself. The book primes the pump and lets the reader go on an inspirational journey