Herbert W. Hamber

HIGHER DERIVATIVE QUANTUM GRAVITY ON A SIMPLICIAL LATTICE

Abstract We generalize the action of Regge calculus to include the equivalent to both a cosmological constant term and a higher derivative term involving the integral of R 2 . We compare our expression for these terms with the continuum values for the regular tessellations of 2-, 3- and 4-dimensional spheres, and describe how the formalism may be applied to calculations in quantum gravity.

Numerical simulations of quantum chromodynamics

Abstract A previously proposed method to perform Monte Carlo simulations with dynamical fermions is applied to lattice QCD. The main features of the computational technique are reviewed and results for some selected quantities, such as the average plaquette action and the quark condensate 〈 ψ ψ〉 are presented. Both the dependence on the quark mass and on the number of flavors are considered. An estimate of the scale parameter in the presence of fermions is given.

Quantum gravitation : the Feynman path integral approach

Continuum Formulation.- Feynman Path Integral Formulation.- Gravity in 2+? Dimensions.- Hamiltonian and Wheeler-DeWitt Equation.- Semiclassical Gravity.- Lattice Regularized Quantum Gravity.- Analytical Lattice Expansion Methods.- Numerical Studies.- Scale Dependent Gravitational Couplings.

CONSIDERATIONS ON NUMERICAL ANALYSIS OF QCD

Abstract We discuss the strategy to remove the quenched approximation and to minimize systematical and statistical errors occurring in the numerical simulation of lattice QCD. We suggest a way to compute the flavour singlet sector of the mass spectrum, and comment about the relation between the fluctuations of the mass values and the scattering amplitudes.

Some predictions for an improved fermion action on the lattice

Abstract We propose an improved fermion action on the lattice by adding a next nearest neightbor interaction term to Wilson action. The proposed action is expected to approach the continuum limit more rapidly. Using the improved action, the predictions for the critical value of the hopping parameter at weak and strong coupling are given. The relationship between quark masses on the lattice and in the continuum is also discussed.

On the quantum corrections to the newtonian potential

Abstract The leading long-distance quantum correction to the Newtonian potential for heavy spinless particles is computed in quantum gravity. The potential is obtained directly from the sum of all graviton exchange diagrams contributing to lowest non-trivial order to the scattering amplitude. The calculation correctly reproduces the leading classical relativistic post-Newtonian correction. The sign of the perturbative quantum correction would indicate that, in the absence of a cosmological constant, quantum effects lead to a slow increase of the gravitational coupling with distance.

Simplicial quantum gravity with higher derivative terms: Formalism and numerical results in four dimensions☆

Abstract Higher derivative terms for Regges formulation of lattice gravity are discussed. The analytic weak-field expansion for the regular tessellation α5 of the four-sphere is presented. Preliminary numerical results for some computations in four dimensions are also discussed.

Nonlocal effective gravitational field equations and the running of Newton's constant G

Non-perturbative studies of quantum gravity have recently suggested the possibility that the strength of gravitational interactions might slowly increase with distance. Here a set of generally covariant effective field equations are proposed, which are intended to incorporate the gravitational, vacuum-polarization induced, running of Newton’s constant G. One attractive feature of this approach is that, from an underlying quantum gravity perspective, the resulting long distance (or large time) effective gravitational action inherits only one adjustable parameter ξ, having the units of a length, arising from dimensional transmutation in the gravitational sector. Assuming the above scenario to be correct, some simple predictions for the long distance corrections to the classical standard model Robertson-Walker metric are worked out in detail, with the results formulated as much as possible in a model-independent framework. It is found that the theory, even in the limit of vanishing renormalized cosmological constant, generally predicts an accelerated power-law expansion at later times t ∼ ξ ∼ 1/H.

Newtonian potential in quantum Regge gravity

We show how the Newtonian potential between two heavy masses can be computed in simplicial quantum gravity. On the lattice we compute correlations between Wilson lines associated with the heavy particles and which are closed by the lattice periodicity. We check that the continuum analog of this quantity reproduces the Newtonian potential in the weak field expansion. In the smooth anti-de Sitter-like phase, which is the only phase where a sensible lattice continuum limit can be constructed in this model, we attempt to determine the shape and mass dependence of the attractive potential close to the critical point in G. It is found that non-linear graviton interactions give rise to a potential which is Yukawa-like, with a mass parameter that decreases towards the critical point where the average curvature vanishes. In the vicinity of the critical point we give an estimate for the effective Newton constant.

Quantum gravity on the lattice

I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity and other non-renormalizable theories, I discuss the general methods and goals of the lattice approach. An underlying theme is the attempt at establishing connections between the continuum renormalization group results, which are mainly based on diagrammatic perturbation theory, and the recent lattice results, which apply to the strong gravity regime and are inherently non-perturbative. A second theme in this review is the ever-present natural correspondence between infrared methods of strongly coupled non-abelian gauge theories on the one hand, and the low energy approach to quantum gravity based on the renormalization group and universality of critical behavior on the other. Towards the end of the review I discuss possible observational consequences of path integral quantum gravity, as derived from the non-trivial ultraviolet fixed point scenario. I argue that the theoretical framework naturally leads to considering a weakly scale-dependent Newton’s constant, with a scaling violation parameter related to the observed scaled cosmological constant (and not, as naively expected, to the Planck length).