The Extended Loop Representation of Quantum Gravity

A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum Gravity can be realized on the state space of extended loop dependent wavefunctions. The extended representation generalizes the loop representation and contains this representation as a particular case. The resulting diffeomorphism and hamiltonian constraints take a very simple form and allow to apply functional methods and simplify the loop calculus. In particular we show that the constraints are linear in the momenta. The nondegenerate solutions known in the loop representation are also solutions of the constraints in the new representation. The practical calculation advantages allows to find a new solution to the Wheeler-DeWitt equation. Moreover, the extended representation puts in a precise framework some of the regularization problems of the loop representation. We show that the solutions are generalized knot invariants, smooth in the extended variables, and any framing is unnecessary.Comment: 27 pages, report IFFC/94-1

Is the third coefficient of the Jones knot polynomial a quantum state of gravity?

Some time ago it was conjectured that the coefficients of an expansion of the Jones polynomial in terms of the cosmological constant could provide an infinite string of knot invariants that are solutions of the vacuum Hamiltonian constraint of quantum gravity in the loop representation. Here we discuss the status of this conjecture at third order in the cosmological constant. The calculation is performed in the extended loop representation, a generalization of the loop representation. It is shown that the the Hamiltonian does not annihilate the third coefficient of the Jones polynomal ($J_3$) for general extended loops. For ordinary loops the result acquires an interesting geometrical meaning and new possibilities appear for $J_3$ to represent a quantum state of gravity.Comment: 22 page

Extended Loops: A New Arena for Nonperturbative Quantum Gravity

We propose a new representation for gauge theories and quantum gravity. It can be viewed as a generalization of the loop representation. We make use of a recently introduced extension of the group of loops into a Lie Group. This extension allows the use of functional methods to solve the constraint equations. It puts in a precise framework the regularization problems of the loop representation. It has practical advantages in the search for quantum states. We present new solutions to the Wheeler-DeWitt equation that reinforce the conjecture that the Jones Polynomial is a state of nonperturbative quantum gravity.Comment: 12pp, Revtex, no figures, CGPG-93/12-

Effect of carrier recombination on ultrafast carrier dynamics in thin films of the topological insulator Bi2Se3

Transient reflectivity (TR) from thin films (6 - 40 nm thick) of the topological insulator Bi2Se3 reveal ultrafast carrier dynamics, which suggest the existence of both radiative and non-radiative recombination between electrons residing in the upper cone of initially unoccupied high energy Dirac surface states (SS) and holes residing in the lower cone of occupied low energy Dirac SS. The modeling of measured TR traces allowed us to conclude that recombination is induced by the depletion of bulk electrons in films below ~20 nm thick due to the charge captured on the surface defects. We predict that such recombination processes can be observed using time-resolved photoluminescence techniques

Classical Loop Actions of Gauge Theories

Since the first attempts to quantize Gauge Theories and Gravity in the loop representation, the problem of the determination of the corresponding classical actions has been raised. Here we propose a general procedure to determine these actions and we explicitly apply it in the case of electromagnetism. Going to the lattice we show that the electromagnetic action in terms of loops is equivalent to the Wilson action, allowing to do Montecarlo calculations in a gauge invariant way. In the continuum these actions need to be regularized and they are the natural candidates to describe the theory in a ``confining phase''.Comment: LaTeX 14 page

Proximal changes in signal transduction that modify CD8+ T cell responsiveness in vivo

The antigen dose conditions the functional properties of CD8+ T cells generated after priming. At relatively low antigen doses, efficient memory T cells may be generated, while high antigen doses lead to tolerance. To determine the mechanisms leading to such different functional outcomes, we compared the proximal TCR signal transduction of naive cells, to that of memory or high-dose tolerant cells generated in vivo. In vivo activation led to the constitutive phosphorylation of CD3 4 , recruiting Zap70, in both memory and tolerant cells. In tolerant cells, these phenomena were much more marked, the CD3 4 and ´ chains no longer associated, and the Src kinases p56Lck and p59Fyn were inactive. Therefore, when the antigen load overcomes the capacities of immune control, a new mechanism intervenes to block signal transduction: the recruitment of Zap70 to CD3 4 becomes excessive, leading to TCR complex destabilization, Src kinase dysfunction, and signal arrest

Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure

We generalize the idea of Vassiliev invariants to the spin network context, with the aim of using these invariants as a kinematical arena for a canonical quantization of gravity. This paper presents a detailed construction of these invariants (both ambient and regular isotopic) requiring a significant elaboration based on the use of Chern-Simons perturbation theory which extends the work of Kauffman, Martin and Witten to four-valent networks. We show that this space of knot invariants has the crucial property -from the point of view of the quantization of gravity- of being loop differentiable in the sense of distributions. This allows the definition of diffeomorphism and Hamiltonian constraints. We show that the invariants are annihilated by the diffeomorphism constraint. In a companion paper we elaborate on the definition of a Hamiltonian constraint, discuss the constraint algebra, and show that the construction leads to a consistent theory of canonical quantum gravity.Comment: 21 Pages, RevTex, many figures included with psfi

The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space

A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic properties of this new mathematical structure are analized in detail. Applications of the formalism to field theory, quantum gravity and knot theory are considered.Comment: The resubmited paper contains the title and abstract, that were omitted in the previous version. 42 pages, report IFFI/93.0

A generalized Hamiltonian Constraint Operator in Loop Quantum Gravity and its simplest Euclidean Matrix Elements

We study a generalized version of the Hamiltonian constraint operator in nonperturbative loop quantum gravity. The generalization is based on admitting arbitrary irreducible SU(2) representations in the regularization of the operator, in contrast to the original definition where only the fundamental representation is taken. This leads to a quantization ambiguity and to a family of operators with the same classical limit. We calculate the action of the Euclidean part of the generalized Hamiltonian constraint on trivalent states, using the graphical notation of Temperley-Lieb recoupling theory. We discuss the relation between this generalization of the Hamiltonian constraint and crossing symmetry.Comment: 35 pp, 20 eps figures; minor corrections, references added; version to appear in Class. Quant. Gra

broadband visible light emission from nominally undoped and hbox cr 3 doped garnet nanopowders

Synthetic garnet nanopowders of Y 3 Al 5 O 12 (YAG) and Gd 3 Ga 5 O 12 (GGG) were produced, and the occurrence of a broadband bright visible emission by nominally undoped YAG and GGG and Cr 3+ doped GGG, depending on the environment pressure, as well as exciting on the pumping power, was demonstrated. The results indicate that high-intensity infrared laser irradiation in samples not only leads to heating (melting effects) but also produces visible broadband emission. Low pressure of the powders' environment favors the white light emission by lowering the threshold pumping power. A hypothesis on the nature of the emission is presented