Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity

The G -->0 limit of Euclidean gravity introduced by Smolin is described by a generally covariant U(1)xU(1)xU(1) gauge theory. The Poisson bracket algebra of its Hamiltonian and diffeomorphism constraints is isomorphic to that of gravity. Motivated by recent results in Parameterized Field Theory and by the search for an anomaly-free quantum dynamics for Loop Quantum Gravity (LQG), the quantum Hamiltonian constraint of density weight 4/3 for this U(1)xU(1)xU(1) theory is constructed so as to produce a non-trivial LQG-type representation of its Poisson brackets through the following steps. First, the constraint at finite triangulation, as well as the commutator between a pair of such constraints, are constructed as operators on the `charge' network basis. Next, the continuum limit of the commutator is evaluated with respect to an operator topology defined by a certain space of `vertex smooth' distributions. Finally, the operator corresponding to the Poisson bracket between a pair of Hamiltonian constraints is constructed at finite triangulation in such a way as to generate a `generalised' diffeomorphism and its continuum limit is shown to agree with that of the commutator between a pair of finite triangulation Hamiltonian constraints. Our results in conjunction with the recent work of Henderson, Laddha and Tomlin in a 2+1-dimensional context, constitute the necessary first steps toward a satisfactory treatment of the quantum dynamics of this model.Comment: 57 pages, 9 figure

Inequivalent coherent state representations in group field theory

In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with infinite number of degrees of freedom on compact base manifolds. We also show that these representations break translation symmetry. Since such representations can be regarded as quantum gravitational systems with an infinite number of fundamental pre-geometric building blocks, they may be more suitable for the description of effective geometrical phases of the theory

Quantum matter in quantum space-time

Quantum matter in quantum space-time is discussed using general properties of energy-conservation laws. As a rather radical conclusion, it is found that standard methods of differential geometry and quantum field theory on curved space-time are inapplicable in canonical quantum gravity, even at the level of effective equations.Comment: 17 pages, v2: further references and more detailed conclusion

Constraint algebra in LQG reloaded : Toy model of a U(1)^{3} Gauge Theory I

We analyze the issue of anomaly-free representations of the constraint algebra in Loop Quantum Gravity (LQG) in the context of a diffeomorphism-invariant gauge theory in three spacetime dimensions. We construct a Hamiltonian constraint operator whose commutator matches with a quantization of the classical Poisson bracket involving structure functions. Our quantization scheme is based on a geometric interpretation of the Hamiltonian constraint as a generator of phase space-dependent diffeomorphisms. The resulting Hamiltonian constraint at finite triangulation has a conceptual similarity with the "mu-bar"-scheme in loop quantum cosmology and highly intricate action on the spin-network states of the theory. We construct a subspace of non-normalizable states (distributions) on which the continuum Hamiltonian constraint is defined which leads to an anomaly-free representation of the Poisson bracket of two Hamiltonian constraints in loop quantized framework.Comment: 60 pages, 6 figure

Self-control enhancement in children:Ethical and conceptual aspects

Childhood self-control is currently receiving great scientific and public attention because it could predict much of adult’s life success and well-being. Specialized interventions based on findings in social psychology and neuroscience potentially enhance children’s capacity to exercise self-control. This perspective triggers hopes that self-control enhancement allows us to say good-bye for good to potentially unsafe psychopharmacological agents and electronic brain stimulants. This chapter provides an in-depth ethical analysis of pediatric self-control enhancement and points toward a series of serious conceptual and ethical concerns. First, it gives an overview of current psychological as well as neuroscientific research on self-control, and it presents longitudinal studies that emphasize the importance of childhood self-control for adult life success. Second, it critically discusses the concept of self-control presupposed in these approaches and points to crucial limitations. Going beyond an understanding of self-control as a sophisticated means of goal-achievement, i will argue for a comprehensive understanding that takes the inherent normativity of self-controlled behavior seriously. In that context, self-control enhancement appears as not necessarily desirable and occasionally even detrimental. Finally, this chapter questions the notion of childhood implicit in current research and how values typically put on this phase of life could get affected by self-control enhancement. I finish with an exploration of the conditions under which pediatric self-control enhancement is either impermissible, permissible, or maybe obligatory

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion