Closed-Flux Solutions to the Constraints for Plane Gravity Waves

The metric for plane gravitational waves is quantized within the Hamiltonian framework, using a Dirac constraint quantization and the self-dual field variables proposed by Ashtekar. The z axis (direction of travel of the waves) is taken to be the entire real line rather than the torus (manifold coordinatized by (z,t) is RxR rather than $S_1$ x R). Solutions to the constraints proposed in a previous paper involve open-ended flux lines running along the entire z axis, rather than closed loops of flux; consequently, these solutions are annihilated by the Gauss constraint at interior points of the z axis, but not at the two boundary points. The solutions studied in the present paper are based on closed flux loops and satisfy the Gauss constraint for all z.Comment: 18 pages; LaTe

Plane waves in quantum gravity: breakdown of the classical spacetime

Starting with the Hamiltonian formulation for spacetimes with two commuting spacelike Killing vectors, we construct a midisuperspace model for linearly polarized plane waves in vacuum gravity. This model has no constraints and its degrees of freedom can be interpreted as an infinite and continuous set of annihilation and creation like variables. We also consider a simplified version of the model, in which the number of modes is restricted to a discrete set. In both cases, the quantization is achieved by introducing a Fock representation. We find regularized operators to represent the metric and discuss whether the coherent states of the quantum theory are peaked around classical spacetimes. It is shown that, although the expectation value of the metric on Killing orbits coincides with a classical solution, its relative fluctuations become significant when one approaches a region where null geodesics are focused. In that region, the spacetimes described by coherent states fail to admit an approximate classical description. This result applies as well to the vacuum of the theory.Comment: 11 pages, no figures, version accepted for publication in Phys. Rev.

Bridging the gap:human emotions and animal emotions

Our experiences of the conscious mental states that we call emotions drive our interest in whether such states also exist in other animals. Because linguistic report can be used as a gold standard (albeit indirect) indicator of subjective emotional feelings in humans but not other species, how can we investigate animal emotions and what exactly do we mean when we use this term? Linguistic reports of human emotion give rise to emotion concepts (discrete emotions; dimensional models), associated objectively measurable behavioral and bodily emotion indicators, and understanding of the emotion contexts that generate specific states. We argue that many animal studies implicitly translate human emotion concepts, indicators and contexts, but that explicit consideration of the underlying pathways of inference, their theoretical basis, assumptions, and pitfalls, and how they relate to conscious emotional feelings, is needed to provide greater clarity and less confusion in the conceptualization and scientific study of animal emotion

Energy and directional signatures for plane quantized gravity waves

Solutions are constructed to the quantum constraints for planar gravity (fields dependent on z and t only) in the Ashtekar complex connection formalism. A number of operators are constructed and applied to the solutions. These include the familiar ADM energy and area operators, as well as new operators sensitive to directionality (z+ct vs. z-ct dependence). The directionality operators are quantum analogs of the classical constraints proposed for unidirectional plane waves by Bondi, Pirani, and Robinson (BPR). It is argued that the quantum BPR constraints will predict unidirectionality reliably only for solutions which are semiclassical in a certain sense. The ADM energy and area operators are likely to have imaginary eigenvalues, unless one either shifts to a real connection, or allows the connection to occur other than in a holonomy. In classical theory, the area can evolve to zero. A quantum mechanical mechanism is proposed which would prevent this collapse.Comment: 54 pages; LaTe

Quantization of pure gravitational plane waves

Pure gravitational plane waves are considered as a special case of spacetimes with two commuting spacelike Killing vector fields. Starting with a midisuperspace that describes this kind of spacetimes, we introduce gauge-fixing and symmetry conditions that remove all non-physical degrees of freedom and ensure that the classical solutions are plane waves. In this way, we arrive at a reduced model with no constraints and whose only degrees of freedom are given by two fields. In a suitable coordinate system, the reduced Hamiltonian that generates the time evolution of this model turns out to vanish, so that all relevant information is contained in the symplectic structure. We calculate this symplectic structure and particularize our discussion to the case of linearly polarized plane waves. The reduced phase space can then be described by an infinite set of annihilation and creation like variables. We finally quantize the linearly polarized model by introducing a Fock representation for these variables.Comment: 11 pages, Revtex, no figure

Projective Invariance and One-Loop Effective Action in Affine-Metric Gravity Interacting with Scalar Field

We investigate the influence of the projective invariance on the renormalization properties of the theory. One-loop counterterms are calculated in the most general case of interaction of gravity with scalar field.Comment: 10 pages, LATE

Dissecting the links between reward and loss, decision-making, and self-reported affect using a computational approach

Links between affective states and risk-taking are often characterised using summary statistics from serial decision-making tasks. However, our understanding of these links, and the utility of decision-making as a marker of affect, needs to accommodate the fact that ongoing (e.g., within-task) experience of rewarding and punishing decision outcomes may alter future decisions and affective states. To date, the interplay between affect, ongoing reward and punisher experience, and decision-making has received little detailed investigation. Here, we examined the relationships between reward and loss experience, affect, and decision-making in humans using a novel judgement bias task analysed with a novel computational model. We demonstrated the influence of within-task favourability on decision-making, with more risk-averse/'pessimistic' decisions following more positive previous outcomes and a greater current average earning rate. Additionally, individuals reporting more negative affect tended to exhibit greater risk-seeking decision-making, and, based on our model, estimated time more poorly. We also found that individuals reported more positive affective valence during periods of the task when prediction errors and offered decision outcomes were more positive. Our results thus provide new evidence that (short-term) within-task rewarding and punishing experiences determine both future decision-making and subjectively experienced affective states