Space-time Structures from Critical Values in 2D Quantum Gravity

A model for 2D Quantum Gravity is constructed out of the Virasoro group. To this end the quantization of the abstract Virasoro group is revisited. For the critical values of the conformal anomaly c, some quantum operators (SL(2,R) generators) lose their dynamical content (they are no longer conjugated operators). The notion of space-time itself in 2D gravity then arises as associated with this kinematical SL(2,R) symmetry. An ensemble of different copies of AdS do co-exist in this model with different weights, depending on their curvature (which is proportional to \hbar^{2}) and they are connected by gravity operators. This model suggests that, in general, quantum diffemorphisms should not be imposed as constraints to the theory, except for the classical limit.Comment: 22 pages, latex, no figures. Revised version with an effort in the development of the underlying classical theory and the clarification of the classical limit. To appear in Class. Quant. Gra

Group Approach to the Quantization of the P\"oschl-Teller dynamics

The quantum dynamics of a particle in the Modified P\"oschl-Teller potential is derived from the group $SL(2,R)$ by applying a Group Approach to Quantization (GAQ). The explicit form of the Hamiltonian as well as the ladder operators is found in the enveloping algebra of this basic symmetry group. The present algorithm provides a physical realization of the non-unitary, finite-dimensional, irreducible representations of the $SL(2,R)$ group. The non-unitarity manifests itself in that only half of the states are normalizable, in contrast with the representations of SU(2) where all the states are physical.Comment: 17 pages, LaTe

Harmonic states for the free particle

Different families of states, which are solutions of the time-dependent free Schr\"odinger equation, are imported from the harmonic oscillator using the Quantum Arnold Transformation introduced in a previous paper. Among them, infinite series of states are given that are normalizable, expand the whole space of solutions, are spatially multi-localized and are eigenstates of a suitably defined number operator. Associated with these states new sets of coherent and squeezed states for the free particle are defined representing traveling, squeezed, multi-localized wave packets. These states are also constructed in higher dimensions, leading to the quantum mechanical version of the Hermite-Gauss and Laguerre-Gauss states of paraxial wave optics. Some applications of these new families of states and procedures to experimentally realize and manipulate them are outlined.Comment: 21 pages, 3 figures. Title changed, content added, references adde

Water Footprint and Life Cycle Assessment as approaches to assess potential impacts of products on water consumption: Key learning points from pilot studies on tea and margarine

Water accounting and environmental impact assessment across the product's life cycle is gaining prominence. This paper presents two case studies of applying the Life Cycle Assessment (LCA) and Water Footprint (WF) approaches to tea and margarine. The WF, excluding grey water, of a carton of 50 g tea is 294 L green water and 10 L blue water, and that of a 500 g tub of margarine is 553 L green water, 109 L blue water. The inventory results in the LCA studies (blue water) are 13 L for tea and 114 L for margarine. In the impact assessment phase of WF, Coonoor in Southern India appears as a potential hotspot for tea production, although the water consumed in energy to boil the kettle and by the consumer are also significant. For margarine the main potential hotspot is irrigated sunflower around Zaporizhia in Ukraine. The impact assessment results of LCA for tea causes the water in the consumer use phase to be down-weighted and stresses the contribution from Coonoor due to the higher water scarcity of this region. Similarly the LCA impact assessment of margarine causes the palm oil contribution to be down-weighted due to the low water scarcity of Medan in Indonesia. From these case studies we identify similarities, differences and synergies at both the water accounting and impact assessment levels for both approaches with the purpose of improving and advancing the water resource assessment process

Quantum States of Topologically Massive Electrodynamics and Gravity

The free quantum states of topologically massive electrodynamics and gravity in 2+1 dimensions, are explicitly found. It is shown that in both theories the states are described by infrared-regular polarization tensors containing a regularization phase which depends on the spin. This is done by explicitly realizing the quantum algebra on a functional Hilbert space and by finding the Wightman function to define the scalar product on such a Hilbert space. The physical properties of the states are analyzed defining creation and annihilation operators. For both theories, a canonical and covariant quantization procedure is developed. The higher order derivatives in the gravitational lagrangian are treated by means of a preliminary Dirac procedure. The closure of the Poincar\'e algebra is guaranteed by the infrared-finiteness of the states which is related to the spin of the excitations through the regularization phase. Such a phase may have interesting physical consequences.Comment: 21 page, latex, no figure

Characterization of surface-states in a hollow core photonic crystal fiber

FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOSurface or edge states represent an important class of modes in various photonic crystal systems such as in dielectric topological insulators and in photonic crystal fibers. In the later, strong attenuation peaks in the transmission spectrum are attributed to coupling between surface and core-guided modes. Here, we explore a modified implementation of the spatial and spectral interference method to experimentally characterize surface modes in photonic crystal fibers. Using an external reference and a non-uniform Fourier transform windowing, the obtained spectrogram allows clear observation of anti-crossing behavior at wavelengths in which surface and core modes are strongly coupled. We also detect surface modes with different spatial symmetries, and give insight into mode families couple to the fundamental or high-order core modes, as well as the existence of uncoupled surface modes.26253255432564FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO2013/20180-32015/04113-008/57857-2Sem informação574017/2008-

The Chevreton Tensor and Einstein-Maxwell Spacetimes Conformal to Einstein Spaces

In this paper we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure-radiation type and that it restricts the spacetimes to Petrov types \textbf{N} or \textbf{O}. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on closed form, we settle with giving the integrability conditions in the general case, but we do give new explicit examples of Einstein-Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a $C$-space. The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are conformally $C$-spaces, but none of them are conformal to Einstein spaces.Comment: 22 pages. Corrected equation (12

Graded contractions and bicrossproduct structure of deformed inhomogeneous algebras

A family of deformed Hopf algebras corresponding to the classical maximal isometry algebras of zero-curvature N-dimensional spaces (the inhomogeneous algebras iso(p,q), p+q=N, as well as some of their contractions) are shown to have a bicrossproduct structure. This is done for both the algebra and, in a low-dimensional example, for the (dual) group aspects of the deformation.Comment: LaTeX file, 20 pages. Trivial changes. To appear in J. Phys.

Expansions of algebras and superalgebras and some applications

After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the Inonu-Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32).Comment: Invited lecture delivered at the 'Deformations and Contractions in Mathematics and Physics Workshop', 15-21 January 2006, Mathematisches Forschungsinstitut Oberwolfach, German